Goldston, Daniel A.; Graham, Sidney W.; Panidapu, Apoorva; Pintz, Janos; Schettler, Jordan; Yıldırım, Cem Y. Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II. (English) Zbl 07300432 J. Number Theory 221, 222-231 (2021). MSC: 11N05 11N25 11N36 PDF BibTeX XML Cite \textit{D. A. Goldston} et al., J. Number Theory 221, 222--231 (2021; Zbl 07300432) Full Text: DOI
Ford, Kevin; Konyagin, Sergei Divisibility of the central binomial coefficient \(\binom{2n}{n} \). (English) Zbl 07291888 Trans. Am. Math. Soc. 374, No. 2, 923-953 (2021). MSC: 05A10 11B65 11N25 PDF BibTeX XML Cite \textit{K. Ford} and \textit{S. Konyagin}, Trans. Am. Math. Soc. 374, No. 2, 923--953 (2021; Zbl 07291888) Full Text: DOI
Gómez-Colunga, Andrés; Kavaler, Charlotte; McNew, Nathan; Zhu, Mirilla On the Erdős primitive set conjecture in function fields. (English) Zbl 07276968 J. Number Theory 219, 412-444 (2021). MSC: 11B83 11N25 11T06 PDF BibTeX XML Cite \textit{A. Gómez-Colunga} et al., J. Number Theory 219, 412--444 (2021; Zbl 07276968) Full Text: DOI
Mehdizadeh, Marzieh The multiplication table for smooth integers. (English) Zbl 07276955 J. Number Theory 219, 172-197 (2021). MSC: 11N25 PDF BibTeX XML Cite \textit{M. Mehdizadeh}, J. Number Theory 219, 172--197 (2021; Zbl 07276955) Full Text: DOI
Sanna, Carlo On numbers divisible by the product of their nonzero base \(b\) digits. (English) Zbl 07311137 Quaest. Math. 43, No. 11, 1563-1571 (2020). MSC: 11A63 11N25 PDF BibTeX XML Cite \textit{C. Sanna}, Quaest. Math. 43, No. 11, 1563--1571 (2020; Zbl 07311137) Full Text: DOI
Phong, Bui Minh; Szeidl, Rita Betti On \(q\)-multiplicative functions with special properties. (English) Zbl 07307810 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 51, 179-190 (2020). MSC: 11A07 11A25 11N25 11N64 PDF BibTeX XML Cite \textit{B. M. Phong} and \textit{R. B. Szeidl}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 51, 179--190 (2020; Zbl 07307810) Full Text: Link
De Koninck, Jean-Marie; Razafindrasoanaivolala, A. Arthur Bonkli On the middle divisors of an integer. (English) Zbl 07307784 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 50, 113-126 (2020). MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{J.-M. De Koninck} and \textit{A. A. B. Razafindrasoanaivolala}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 50, 113--126 (2020; Zbl 07307784) Full Text: Link
De Koninck, Jean-Marie; Kátai, Imre; Phong, Bui Minh Characterising some triplets of completely multiplicative functions. (English) Zbl 07307783 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 50, 101-112 (2020). MSC: 11A07 11A25 11N25 11N64 PDF BibTeX XML Cite \textit{J.-M. De Koninck} et al., Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 50, 101--112 (2020; Zbl 07307783) Full Text: Link
Nyandwi, S.; Smati, A. Distribution laws of friable divisors. (English) Zbl 07306585 Integers 20, Paper A39, 23 p. (2020). MSC: 11N25 PDF BibTeX XML Cite \textit{S. Nyandwi} and \textit{A. Smati}, Integers 20, Paper A39, 23 p. (2020; Zbl 07306585) Full Text: Link
Kinlaw, Paul; Kobayashi, Mitsuo; Pomerance, Carl On the equation \(\varphi(n)=\varphi(n+1)\). (English) Zbl 07301076 Acta Arith. 196, No. 1, 69-92 (2020). MSC: 11N25 11Y99 PDF BibTeX XML Cite \textit{P. Kinlaw} et al., Acta Arith. 196, No. 1, 69--92 (2020; Zbl 07301076) Full Text: DOI
Tangsupphathawat, Pinthira; Srichan, Teerapat; Laohakosol, Vichian Square-full primitive roots in short intervals. (English) Zbl 07293423 Rad Hrvat. Akad. Znan. Umjet., Mat. Znan. 542(24), 39-48 (2020). MSC: 11L07 11N25 11N69 PDF BibTeX XML Cite \textit{P. Tangsupphathawat} et al., Rad Hrvat. Akad. Znan. Umjet., Mat. Znan. 542(24), 39--48 (2020; Zbl 07293423) Full Text: DOI
Li, Xiumei; Sha, Min A proof of Sondow’s conjecture on the Smarandache function. (English) Zbl 07286906 Am. Math. Mon. 127, No. 10, 939-943 (2020). MSC: 11A25 11N25 PDF BibTeX XML Cite \textit{X. Li} and \textit{M. Sha}, Am. Math. Mon. 127, No. 10, 939--943 (2020; Zbl 07286906) Full Text: DOI
Saha, Biswajyoti; Sankaranarayanan, Ayyadurai; Suzuki, Yuta An asymptotic formula and some explicit estimates of the counting function of \(y\)-friable numbers. (English) Zbl 07283194 Mishou, Hidehiko (ed.) et al., Various aspects of multiple zeta functions – in honor of Professor Kohji Matsumoto’s 60th birthday. Proceedings of the international conference, Nagoya University, Nagoya, Japan August 21–25, 2020. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-088-4/hbk). Advanced Studies in Pure Mathematics 84, 367-397 (2020). MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{B. Saha} et al., Adv. Stud. Pure Math. 84, 367--397 (2020; Zbl 07283194) Full Text: DOI Euclid
Sittinger, Brian D.; DeMoss, Ryan D. The probability that ideals in a number ring are \(k\)-wise relatively \(r\)-prime. (English) Zbl 1444.11194 Int. J. Number Theory 16, No. 8, 1753-1765 (2020). MSC: 11N25 11R45 11R04 PDF BibTeX XML Cite \textit{B. D. Sittinger} and \textit{R. D. DeMoss}, Int. J. Number Theory 16, No. 8, 1753--1765 (2020; Zbl 1444.11194) Full Text: DOI
Kerr, Bryce; Shparlinski, Igor E.; Yau, Kam Hung A refinement of the burgess bound for character sums. (English) Zbl 07244370 Mich. Math. J. 69, No. 2, 227-240 (2020). MSC: 11L40 11N25 PDF BibTeX XML Cite \textit{B. Kerr} et al., Mich. Math. J. 69, No. 2, 227--240 (2020; Zbl 07244370) Full Text: DOI Euclid
Kobayashi, Mits; Trudgian, Tim On integers \(n\) for which \(\sigma (2n + 1) \geq \sigma (2n)\). (English) Zbl 07226720 J. Number Theory 215, 138-148 (2020). MSC: 11A25 11N25 PDF BibTeX XML Cite \textit{M. Kobayashi} and \textit{T. Trudgian}, J. Number Theory 215, 138--148 (2020; Zbl 07226720) Full Text: DOI
Munsch, Marc; Shparlinski, Igor E. On smooth square-free numbers in arithmetic progressions. (English) Zbl 07226674 J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041-1067 (2020). MSC: 11N25 11B25 11L40 PDF BibTeX XML Cite \textit{M. Munsch} and \textit{I. E. Shparlinski}, J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041--1067 (2020; Zbl 07226674) Full Text: DOI
Cohen, Peter; Cordwell, Katherine; Epstein, Alyssa; Kwan, Chung-Hang; Lott, Adam; Miller, Steven J. On near-perfect numbers. (English) Zbl 07221822 Acta Arith. 194, No. 4, 341-366 (2020). MSC: 11A25 11N25 11B83 PDF BibTeX XML Cite \textit{P. Cohen} et al., Acta Arith. 194, No. 4, 341--366 (2020; Zbl 07221822) Full Text: DOI
Dimitrov, Stoyan On the number of pairs of positive integers \(x, y \leq H\) such that \(x^2+y^2+1, x^2+y^2+2\) are square-free. (English) Zbl 07221818 Acta Arith. 194, No. 3, 281-294 (2020). MSC: 11L05 11N25 11N37 PDF BibTeX XML Cite \textit{S. Dimitrov}, Acta Arith. 194, No. 3, 281--294 (2020; Zbl 07221818) Full Text: DOI
Vatwani, Akshaa; Wong, Peng-Jie On generalizations of the Titchmarsh divisor problem. (English) Zbl 07221799 Acta Arith. 193, No. 4, 321-337 (2020). MSC: 11N37 11N25 PDF BibTeX XML Cite \textit{A. Vatwani} and \textit{P.-J. Wong}, Acta Arith. 193, No. 4, 321--337 (2020; Zbl 07221799) Full Text: DOI
Chang, Ben; Martin, Greg The smallest invariant factor of the multiplicative group. (English) Zbl 07219277 Int. J. Number Theory 16, No. 6, 1377-1405 (2020). MSC: 11N25 11N37 11N45 11N64 20K01 PDF BibTeX XML Cite \textit{B. Chang} and \textit{G. Martin}, Int. J. Number Theory 16, No. 6, 1377--1405 (2020; Zbl 07219277) Full Text: DOI
Musin, Oleg R. Ramanujan’s theorem and highest abundant numbers. (English) Zbl 1445.11098 Arnold Math. J. 6, No. 1, 119-130 (2020). MSC: 11N25 11M26 PDF BibTeX XML Cite \textit{O. R. Musin}, Arnold Math. J. 6, No. 1, 119--130 (2020; Zbl 1445.11098) Full Text: DOI
Ford, Kevin; Qian, Guoyou The distribution of divisors of polynomials. (English) Zbl 1453.11122 Mathematika 66, No. 2, 395-415 (2020). MSC: 11N32 11N25 PDF BibTeX XML Cite \textit{K. Ford} and \textit{G. Qian}, Mathematika 66, No. 2, 395--415 (2020; Zbl 1453.11122) Full Text: DOI
Munsch, Marc; Shparlinski, Igor E.; Yau, Kam Hung Smooth squarefree and squarefull integers in arithmetic progressions. (English) Zbl 1446.11174 Mathematika 66, No. 1, 56-70 (2020). Reviewer: Krassimir Atanassov (Sofia) MSC: 11N25 11B25 11L05 11L40 PDF BibTeX XML Cite \textit{M. Munsch} et al., Mathematika 66, No. 1, 56--70 (2020; Zbl 1446.11174) Full Text: DOI
Saad Eddin, Sumaia; Suzuki, Yuta On the distribution of products of two primes. (English) Zbl 1446.11175 J. Number Theory 214, 100-136 (2020). Reviewer: Gennady Bachman (Las Vegas) MSC: 11N25 11N69 PDF BibTeX XML Cite \textit{S. Saad Eddin} and \textit{Y. Suzuki}, J. Number Theory 214, 100--136 (2020; Zbl 1446.11175) Full Text: DOI
Wu, X.-H. Special forms and the distribution of practical numbers. (English) Zbl 1449.11096 Acta Math. Hung. 160, No. 2, 405-411 (2020). Reviewer: Thomas B. Ward (Leeds) MSC: 11N25 PDF BibTeX XML Cite \textit{X. H. Wu}, Acta Math. Hung. 160, No. 2, 405--411 (2020; Zbl 1449.11096) Full Text: DOI
Gómez-Colunga, Andrés; Kavaler, Charlotte; McNew, Nathan; Zhu, Mirilla On the size of primitive sets in function fields. (English) Zbl 07189005 Finite Fields Appl. 64, Article ID 101658, 23 p. (2020). Reviewer: Mehdi Hassani (Zanjan) MSC: 11T55 11N25 11B05 PDF BibTeX XML Cite \textit{A. Gómez-Colunga} et al., Finite Fields Appl. 64, Article ID 101658, 23 p. (2020; Zbl 07189005) Full Text: DOI
Lichtman, Jared Duker Almost primes and the Banks-Martin conjecture. (English) Zbl 1437.11136 J. Number Theory 211, 513-529 (2020). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N25 11Y60 11A05 11M32 PDF BibTeX XML Cite \textit{J. D. Lichtman}, J. Number Theory 211, 513--529 (2020; Zbl 1437.11136) Full Text: DOI
Sanna, Carlo On the number of distinct exponents in the prime factorization of an integer. (English) Zbl 1439.11245 Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 27, 11 p. (2020). MSC: 11N25 11N37 11N64 PDF BibTeX XML Cite \textit{C. Sanna}, Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 27, 11 p. (2020; Zbl 1439.11245) Full Text: DOI
Weingartner, Andreas The constant factor in the asymptotic for practical numbers. (English) Zbl 07182437 Int. J. Number Theory 16, No. 3, 629-638 (2020). MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{A. Weingartner}, Int. J. Number Theory 16, No. 3, 629--638 (2020; Zbl 07182437) Full Text: DOI
Korolev, Maxim; Shparlinski, Igor Sums of algebraic trace functions twisted by arithmetic functions. (English) Zbl 07179068 Pac. J. Math. 304, No. 2, 505-522 (2020). MSC: 11L05 11N25 11T23 PDF BibTeX XML Cite \textit{M. Korolev} and \textit{I. Shparlinski}, Pac. J. Math. 304, No. 2, 505--522 (2020; Zbl 07179068) Full Text: DOI
Akbal, Yıldırım A note on values of Beatty sequences that are free of large prime factors. (English) Zbl 07178817 Colloq. Math. 160, No. 1, 53-63 (2020). MSC: 11N25 11L03 PDF BibTeX XML Cite \textit{Y. Akbal}, Colloq. Math. 160, No. 1, 53--63 (2020; Zbl 07178817) Full Text: DOI
Hajdu, L.; Sárközy, A. On multiplicative decompositions of polynomial sequences. III. (English) Zbl 1447.11099 Acta Arith. 193, No. 2, 193-216 (2020). Reviewer: Florian Luca (Johannesburg) MSC: 11N25 11N32 11D41 PDF BibTeX XML Cite \textit{L. Hajdu} and \textit{A. Sárközy}, Acta Arith. 193, No. 2, 193--216 (2020; Zbl 1447.11099) Full Text: DOI
Luca, Florian; Moodley, Damon Composite positive integers whose sum of prime factors is prime. (English) Zbl 07177880 Arch. Math., Brno 56, No. 1, 49-64 (2020). MSC: 11N25 11N36 PDF BibTeX XML Cite \textit{F. Luca} and \textit{D. Moodley}, Arch. Math., Brno 56, No. 1, 49--64 (2020; Zbl 07177880) Full Text: DOI
Bober, J. W.; Fretwell, D.; Martin, G.; Wooley, T. D. Smooth values of polynomials. (English) Zbl 07177251 J. Aust. Math. Soc. 108, No. 2, 245-261 (2020). MSC: 11N32 11N25 12E05 PDF BibTeX XML Cite \textit{J. W. Bober} et al., J. Aust. Math. Soc. 108, No. 2, 245--261 (2020; Zbl 07177251) Full Text: DOI
Liu, Jianya; Wu, Jie; Xi, Ping Primes in arithmetic progressions with friable indices. (English) Zbl 07175983 Sci. China, Math. 63, No. 1, 23-38 (2020). MSC: 11N05 11N13 11N25 11N36 PDF BibTeX XML Cite \textit{J. Liu} et al., Sci. China, Math. 63, No. 1, 23--38 (2020; Zbl 07175983) Full Text: DOI
Srichan, Teerapat On the distribution of square-full and cube-full primitive roots. (English) Zbl 07175033 Period. Math. Hung. 46, No. 1, 103-107 (2020). MSC: 11N25 11B50 PDF BibTeX XML Cite \textit{T. Srichan}, Period. Math. Hung. 46, No. 1, 103--107 (2020; Zbl 07175033) Full Text: DOI
Tenenbaum, Gérald On local laws for the number of small prime factors. (English) Zbl 07173681 Ramanujan J. 51, No. 1, 153-161 (2020). MSC: 11N25 11N37 11N60 PDF BibTeX XML Cite \textit{G. Tenenbaum}, Ramanujan J. 51, No. 1, 153--161 (2020; Zbl 07173681) Full Text: DOI
Alladi, Krishnaswami; Molnar, Todd The local distribution of the number of small prime factors: variation of the classical theme. (English) Zbl 07173680 Ramanujan J. 51, No. 1, 117-151 (2020). MSC: 11M06 11M41 11N25 11N37 11N60 PDF BibTeX XML Cite \textit{K. Alladi} and \textit{T. Molnar}, Ramanujan J. 51, No. 1, 117--151 (2020; Zbl 07173680) Full Text: DOI
Noguchi, Kazunori Fundamental properties of Björner’s complexes. (English) Zbl 1443.11194 Topology Appl. 272, Article ID 107055, 7 p. (2020). MSC: 11N25 11A05 55U10 PDF BibTeX XML Cite \textit{K. Noguchi}, Topology Appl. 272, Article ID 107055, 7 p. (2020; Zbl 1443.11194) Full Text: DOI
Goudout, Élie Erdős-Kac theorem for integer translates with k prime factors. (Théorème d’Erdős-Kac pour les translatés d’entiers ayant \(k\) facteurs premiers.) (French. English summary) Zbl 07161180 J. Number Theory 210, 280-291 (2020). MSC: 11N25 11N05 11N37 PDF BibTeX XML Cite \textit{É. Goudout}, J. Number Theory 210, 280--291 (2020; Zbl 07161180) Full Text: DOI
Mcnew, Nathan Primitive and geometric-progression-free sets without large gaps. (English) Zbl 07146373 Acta Arith. 192, No. 1, 95-104 (2020). MSC: 11N25 11B05 PDF BibTeX XML Cite \textit{N. Mcnew}, Acta Arith. 192, No. 1, 95--104 (2020; Zbl 07146373) Full Text: DOI arXiv
Jitman, Somphong; Prugsapitak, Supawadee; Raka, Madhu Some generalizations of good integers and their applications in the study of self-dual negacyclic codes. (English) Zbl 07136838 Adv. Math. Commun. 14, No. 1, 35-51 (2020). MSC: 11N25 94B15 94B60 PDF BibTeX XML Cite \textit{S. Jitman} et al., Adv. Math. Commun. 14, No. 1, 35--51 (2020; Zbl 07136838) Full Text: DOI
Leonetti, Paolo; Sanna, Carlo Practical numbers among the binomial coefficients. (English) Zbl 07118781 J. Number Theory 207, 145-155 (2020). Reviewer: Jürgen Spilker (Freiburg im Breisgau) MSC: 11B65 11N25 PDF BibTeX XML Cite \textit{P. Leonetti} and \textit{C. Sanna}, J. Number Theory 207, 145--155 (2020; Zbl 07118781) Full Text: DOI arXiv
Wu, Jie Elliott-Halberstam conjecture and values taken by the largest prime factor of shifted primes. (English) Zbl 07114419 J. Number Theory 206, 282-295 (2020). MSC: 11N05 11N25 11N36 PDF BibTeX XML Cite \textit{J. Wu}, J. Number Theory 206, 282--295 (2020; Zbl 07114419) Full Text: DOI
Goudout, Élie Simultaneous concentrations of additive functions. (Concentrations simultanées de fonctions additives.) (French. English summary) Zbl 1445.11097 J. Théor. Nombres Bordx. 31, No. 2, 385-402 (2019). MSC: 11N25 11N32 11N60 PDF BibTeX XML Cite \textit{É. Goudout}, J. Théor. Nombres Bordx. 31, No. 2, 385--402 (2019; Zbl 1445.11097) Full Text: DOI
Li, Keyao; Liu, Hua’ning On the trace of products of \(k\) elements in finite fields. (Chinese. English summary) Zbl 1449.11094 Pure Appl. Math. 35, No. 4, 394-407 (2019). MSC: 11N25 11N69 PDF BibTeX XML Cite \textit{K. Li} and \textit{H. Liu}, Pure Appl. Math. 35, No. 4, 394--407 (2019; Zbl 1449.11094) Full Text: DOI
Sun, Xue-Gong Primes of the form \(kM^n+n\). (English) Zbl 1449.11095 Acta Math. Hung. 158, No. 1, 100-108 (2019). MSC: 11N25 11N36 PDF BibTeX XML Cite \textit{X.-G. Sun}, Acta Math. Hung. 158, No. 1, 100--108 (2019; Zbl 1449.11095) Full Text: DOI
Chubarikov, Vladimir Nikolaevich The mean value of products of Legendre symbol over primes. (Russian. English summary) Zbl 1434.11194 Chebyshevskiĭ Sb. 20, No. 2(70), 336-347 (2019). MSC: 11N13 11N25 11N36 PDF BibTeX XML Cite \textit{V. N. Chubarikov}, Chebyshevskiĭ Sb. 20, No. 2(70), 336--347 (2019; Zbl 1434.11194) Full Text: DOI MNR
Gromakovskaya, Larisa Aleksandrovna; Shirokov, Boris Mikhaĭlovich Distribution of values of Jordan function in residue classes. (Russian. English summary) Zbl 1434.11197 Chebyshevskiĭ Sb. 20, No. 2(70), 123-139 (2019). MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{L. A. Gromakovskaya} and \textit{B. M. Shirokov}, Chebyshevskiĭ Sb. 20, No. 2(70), 123--139 (2019; Zbl 1434.11197) Full Text: DOI MNR
Srichan, Teerapat; Tangsupphathawat, Pinthira On the distribution of primitive roots that are \((k,r)\)-integers. (English) Zbl 1447.11004 Armen. J. Math. 11, Paper No. 12, 12 p. (2019). Reviewer: Huaning Liu (Xi’an) MSC: 11A07 11L40 11N25 PDF BibTeX XML Cite \textit{T. Srichan} and \textit{P. Tangsupphathawat}, Armen. J. Math. 11, Paper No. 12, 12 p. (2019; Zbl 1447.11004) Full Text: Link
Pinsky, Ross G. A natural probabilistic model on the integers and its relation to Dickman-type distributions and Buchstab’s function. (English) Zbl 1430.60029 Friz, Peter (ed.) et al., Probability and analysis in interacting physical systems. In honor of S. R. S. Varadhan. Based on a workshop on the occasion of Varadhan’s 75th birthday, TU Berlin, Germany, August 15–19, 2016. Cham: Springer. Springer Proc. Math. Stat. 283, 267-294 (2019). MSC: 60F05 11N25 11K65 PDF BibTeX XML Cite \textit{R. G. Pinsky}, Springer Proc. Math. Stat. 283, 267--294 (2019; Zbl 1430.60029) Full Text: DOI
Drappeau, Sary; Topacogullari, Berke Combinatorial identities and Titchmarsh’s divisor problem for multiplicative functions. (English) Zbl 07154433 Algebra Number Theory 13, No. 10, 2383-2425 (2019). MSC: 11N37 11N25 PDF BibTeX XML Cite \textit{S. Drappeau} and \textit{B. Topacogullari}, Algebra Number Theory 13, No. 10, 2383--2425 (2019; Zbl 07154433) Full Text: DOI
Dimitrov, S. I. On the distribution of consecutive square-free numbers of the form \([\alpha n], [\alpha n]+1\). (English) Zbl 1428.11163 Proc. Jangjeon Math. Soc. 22, No. 3, 463-470 (2019). MSC: 11N25 11L05 11N37 PDF BibTeX XML Cite \textit{S. I. Dimitrov}, Proc. Jangjeon Math. Soc. 22, No. 3, 463--470 (2019; Zbl 1428.11163) Full Text: DOI
Granville, Andrew Number theory revealed: a masterclass. (English) Zbl 07147913 Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4158-6/hbk; 978-1-4704-5424-1/ebook). xxviii, 587 p. (2019). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11A55 11B30 11B39 11D09 11D25 11N05 11N25 PDF BibTeX XML Cite \textit{A. Granville}, Number theory revealed: a masterclass. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 07147913)
Maier, Helmut; Singh, Saurabh Kumar On the set of divisors of Gaussian integers. (English) Zbl 07140968 Ramanujan J. 50, No. 2, 355-366 (2019). MSC: 11N25 11N36 11L03 PDF BibTeX XML Cite \textit{H. Maier} and \textit{S. K. Singh}, Ramanujan J. 50, No. 2, 355--366 (2019; Zbl 07140968) Full Text: DOI
Chern, Shane An extension of a formula of Jovovic. (English) Zbl 07133438 Integers 19, Paper A47, 7 p. (2019). MSC: 11B50 11N25 PDF BibTeX XML Cite \textit{S. Chern}, Integers 19, Paper A47, 7 p. (2019; Zbl 07133438) Full Text: Link
Zacharovas, V. The estimate of \(\chi^2\)-distance between binomial and generalized binomial distributions. (English) Zbl 1441.62057 Theory Probab. Appl. 64, No. 3, 444-455 (2019) and Teor. Veroyatn. Primen. 64, No. 3, 552-565 (2019). Reviewer: Catalin Stoean (Craiova) MSC: 62E15 62G07 60E05 17B63 11K38 11N25 11N60 PDF BibTeX XML Cite \textit{V. Zacharovas}, Theory Probab. Appl. 64, No. 3, 444--455 (2019; Zbl 1441.62057) Full Text: DOI
Sanna, Carlo Practical numbers in Lucas sequences. (English) Zbl 07111866 Quaest. Math. 42, No. 7, 977-983 (2019). Reviewer: Jürgen Spilker (Freiburg im Breisgau) MSC: 11B39 11N25 PDF BibTeX XML Cite \textit{C. Sanna}, Quaest. Math. 42, No. 7, 977--983 (2019; Zbl 07111866) Full Text: DOI
Ao, Lingfeng; Luo, Yuanyuan; Tan, Qianrong Asymptotic behavior of the number of generalized Lehmer numbers. (English) Zbl 1438.11125 J. Sichuan Univ., Nat. Sci. Ed. 56, No. 1, 1-4 (2019). MSC: 11N25 11L05 PDF BibTeX XML Cite \textit{L. Ao} et al., J. Sichuan Univ., Nat. Sci. Ed. 56, No. 1, 1--4 (2019; Zbl 1438.11125) Full Text: DOI
Mahnkopf, J. Book review of: K. Broughan, Equivalents of the Riemann hypothesis. Volume 2: Analytic equivalents. (English) Zbl 1435.00031 Monatsh. Math. 190, No. 2, 406 (2019). MSC: 00A17 11-02 11M26 11N05 11N25 PDF BibTeX XML Cite \textit{J. Mahnkopf}, Monatsh. Math. 190, No. 2, 406 (2019; Zbl 1435.00031) Full Text: DOI
Franze, C. S. A note on an asymptotic expansion related to the Dickman function. (English) Zbl 07096578 Ramanujan J. 49, No. 3, 515-530 (2019). MSC: 11N25 11N99 PDF BibTeX XML Cite \textit{C. S. Franze}, Ramanujan J. 49, No. 3, 515--530 (2019; Zbl 07096578) Full Text: DOI
Wang, Zhiwei (Sur les plus grands facteurs premiers inférieur à \(y\) d’entiers consécutifs.) (French. English summary) Zbl 07096575 Ramanujan J. 49, No. 3, 483-490 (2019). MSC: 11N25 11K65 PDF BibTeX XML Cite \textit{Z. Wang}, Ramanujan J. 49, No. 3, 483--490 (2019; Zbl 07096575) Full Text: DOI
de la Bretèche, Régis; Tenenbaum, Gérald Gál-type sums and applications. (Sommes de Gál et applications.) (French. English summary) Zbl 07094285 Proc. Lond. Math. Soc. (3) 119, No. 1, 104-134 (2019). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11N37 11A05 11L40 11M06 11N25 PDF BibTeX XML Cite \textit{R. de la Bretèche} and \textit{G. Tenenbaum}, Proc. Lond. Math. Soc. (3) 119, No. 1, 104--134 (2019; Zbl 07094285) Full Text: DOI arXiv
Bayless, Jonathan; Kinlaw, Paul; Klyve, Dominic Sums over primitive sets with a fixed number of prime factors. (English) Zbl 07088087 Math. Comput. 88, No. 320, 3063-3077 (2019). MSC: 11N25 11Y55 PDF BibTeX XML Cite \textit{J. Bayless} et al., Math. Comput. 88, No. 320, 3063--3077 (2019; Zbl 07088087) Full Text: DOI
Burek, Dominik; Żmija, Błażej A new upper bound for numbers with the Lehmer property and its application to repunit numbers. (English) Zbl 07085362 Int. J. Number Theory 15, No. 7, 1463-1468 (2019). MSC: 11N25 11B39 PDF BibTeX XML Cite \textit{D. Burek} and \textit{B. Żmija}, Int. J. Number Theory 15, No. 7, 1463--1468 (2019; Zbl 07085362) Full Text: DOI arXiv
Pollack, Paul Popular subsets for Euler’s \(\varphi \)-function. (English) Zbl 1426.11115 Math. Ann. 374, No. 1-2, 253-271 (2019). Reviewer: Nikolaj M. Glazunov (Kyïv) MSC: 11N64 11N25 11N37 PDF BibTeX XML Cite \textit{P. Pollack}, Math. Ann. 374, No. 1--2, 253--271 (2019; Zbl 1426.11115) Full Text: DOI
Anil Kumar, C. P. On the gaps in multiplicatively closed sets generated by at most two elements. (English) Zbl 1448.11021 Proc. Indian Acad. Sci., Math. Sci. 129, No. 3, Paper No. 42, 15 p. (2019). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11B05 11B25 11N25 11N69 PDF BibTeX XML Cite \textit{C. P. Anil Kumar}, Proc. Indian Acad. Sci., Math. Sci. 129, No. 3, Paper No. 42, 15 p. (2019; Zbl 1448.11021) Full Text: DOI
Kinlaw, Paul Lower bounds for numbers with three prime factors. (English) Zbl 1441.11244 Integers 19, Paper A22, 18 p. (2019). Reviewer: Gennady Bachman (Las Vegas) MSC: 11N25 PDF BibTeX XML Cite \textit{P. Kinlaw}, Integers 19, Paper A22, 18 p. (2019; Zbl 1441.11244) Full Text: Link
De Koninck, Jean-Marie; Kátai, Imre On the values of the Euler function around shifted primes. (English. French summary) Zbl 1436.11118 Ann. Math. Qué. 43, No. 1, 37-50 (2019). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N60 11N25 26A15 PDF BibTeX XML Cite \textit{J.-M. De Koninck} and \textit{I. Kátai}, Ann. Math. Qué. 43, No. 1, 37--50 (2019; Zbl 1436.11118) Full Text: DOI
Sanna, Carlo On numbers \(n\) relatively prime to the \(n\)th term of a linear recurrence. (English) Zbl 07066678 Bull. Malays. Math. Sci. Soc. (2) 42, No. 2, 827-833 (2019). MSC: 11B37 11A07 11B39 11N25 PDF BibTeX XML Cite \textit{C. Sanna}, Bull. Malays. Math. Sci. Soc. (2) 42, No. 2, 827--833 (2019; Zbl 07066678) Full Text: DOI arXiv
Kátai, Imre; Phong, Bui Minh On additive arithmetical functions with values in topological groups. III. (English) Zbl 1424.11144 Publ. Math. 94, No. 1-2, 49-54 (2019). Reviewer: Lajos Hajdu (Debrecen) MSC: 11N64 11A25 11N25 PDF BibTeX XML Cite \textit{I. Kátai} and \textit{B. M. Phong}, Publ. Math. 94, No. 1--2, 49--54 (2019; Zbl 1424.11144) Full Text: DOI
Chen, Bin; Wu, Jie On values taken by the largest prime factor of shifted primes (II). (English) Zbl 07063391 Int. J. Number Theory 15, No. 5, 935-944 (2019). MSC: 11N05 11N25 11N36 PDF BibTeX XML Cite \textit{B. Chen} and \textit{J. Wu}, Int. J. Number Theory 15, No. 5, 935--944 (2019; Zbl 07063391) Full Text: DOI
Dartyge, Cécile Friable integers: an overview. (English) Zbl 1414.11108 Eur. Math. Soc. Newsl. 111, 6-13 (2019). MSC: 11N25 11-02 PDF BibTeX XML Cite \textit{C. Dartyge}, Eur. Math. Soc. Newsl. 111, 6--13 (2019; Zbl 1414.11108) Full Text: DOI
Amato, Gianluca; Hasler, Maximilian F.; Melfi, Giuseppe; Parton, Maurizio Primitive abundant and weird numbers with many prime factors. (English) Zbl 1437.11167 J. Number Theory 201, 436-459 (2019). MSC: 11Y55 11N25 11A25 PDF BibTeX XML Cite \textit{G. Amato} et al., J. Number Theory 201, 436--459 (2019; Zbl 1437.11167) Full Text: DOI
Bergelson, Vitaly; Kułaga-Przymus, Joanna; Lemańczyk, Mariusz; Richter, Florian K. A generalization of Kátai’s orthogonality criterion with applications. (English) Zbl 1439.11167 Discrete Contin. Dyn. Syst. 39, No. 5, 2581-2612 (2019). MSC: 11J71 11K06 11N25 37A99 PDF BibTeX XML Cite \textit{V. Bergelson} et al., Discrete Contin. Dyn. Syst. 39, No. 5, 2581--2612 (2019; Zbl 1439.11167) Full Text: DOI
Weingartner, Andreas On the constant factor in several related asymptotic estimates. (English) Zbl 1443.11195 Math. Comput. 88, No. 318, 1883-1902 (2019). MSC: 11N25 11Y60 PDF BibTeX XML Cite \textit{A. Weingartner}, Math. Comput. 88, No. 318, 1883--1902 (2019; Zbl 1443.11195) Full Text: DOI arXiv
Gu, Miao; Martin, Greg Factorization tests and algorithms arising from counting modular forms and automorphic representations. (English) Zbl 1446.11215 Can. Math. Bull. 62, No. 1, 81-97 (2019). MSC: 11Y05 11F70 11N25 11N60 11N75 11Y16 PDF BibTeX XML Cite \textit{M. Gu} and \textit{G. Martin}, Can. Math. Bull. 62, No. 1, 81--97 (2019; Zbl 1446.11215) Full Text: DOI arXiv
Changa, M. E. On integers whose number of prime divisors belongs to a given residue class. (English. Russian original) Zbl 1443.11192 Izv. Math. 83, No. 1, 173-183 (2019); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 1, 192-202 (2019). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{M. E. Changa}, Izv. Math. 83, No. 1, 173--183 (2019; Zbl 1443.11192); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 1, 192--202 (2019) Full Text: DOI
Nguyen, Hanh My; Pomerance, Carl The reciprocal sum of the amicable numbers. (English) Zbl 1429.11009 Math. Comput. 88, No. 317, 1503-1526 (2019). MSC: 11A25 11N25 11N64 PDF BibTeX XML Cite \textit{H. M. Nguyen} and \textit{C. Pomerance}, Math. Comput. 88, No. 317, 1503--1526 (2019; Zbl 1429.11009) Full Text: DOI
Mastrostefano, Daniele; Sanna, Carlo On numbers \(n\) with polynomial image coprime with the \(n\)th term of a linear recurrence. (English) Zbl 07000015 Bull. Aust. Math. Soc. 99, No. 1, 23-33 (2019). MSC: 11B37 11A07 11B39 11N25 PDF BibTeX XML Cite \textit{D. Mastrostefano} and \textit{C. Sanna}, Bull. Aust. Math. Soc. 99, No. 1, 23--33 (2019; Zbl 07000015) Full Text: DOI arXiv
Shparlinski, Igor E. On short products of primes in arithmetic progressions. (English) Zbl 06998133 Proc. Am. Math. Soc. 147, No. 3, 977-986 (2019). MSC: 11N25 11B25 11L07 11N36 PDF BibTeX XML Cite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 147, No. 3, 977--986 (2019; Zbl 06998133) Full Text: DOI arXiv
Maier, Helmut; Singh, Saurabh Kumar On multiplicative functions with mean-value close to \(-1\) on primes. (English) Zbl 1415.11119 J. Number Theory 197, 89-105 (2019). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11N36 11L03 PDF BibTeX XML Cite \textit{H. Maier} and \textit{S. K. Singh}, J. Number Theory 197, 89--105 (2019; Zbl 1415.11119) Full Text: DOI
Pollack, Paul How often is Euler’s totient a perfect power? (English) Zbl 1411.11092 J. Number Theory 197, 1-12 (2019). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N64 11N25 11N37 PDF BibTeX XML Cite \textit{P. Pollack}, J. Number Theory 197, 1--12 (2019; Zbl 1411.11092) Full Text: DOI
Matomäki, Kaisa; Radziwiłł, Maksym Multiplicative functions in short intervals, and correlations of multiplicative functions. (English) Zbl 1443.11193 Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume II. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 321-343 (2018). MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{K. Matomäki} and \textit{M. Radziwiłł}, in: Proceedings of the international congress of mathematicians, ICM 2018, Rio de Janeiro, Brazil, August 1--9, 2018. Volume II. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 321--343 (2018; Zbl 1443.11193) Full Text: DOI
Frantzikinakis, Nikos An averaged Chowla and Elliott conjecture along independent polynomials. (English) Zbl 1440.11185 Int. Math. Res. Not. 2018, No. 12, 3721-3743 (2018). MSC: 11N37 11N25 37A44 PDF BibTeX XML Cite \textit{N. Frantzikinakis}, Int. Math. Res. Not. 2018, No. 12, 3721--3743 (2018; Zbl 1440.11185) Full Text: DOI arXiv
Dimitrov, S. I. Consecutive square-free numbers of the form \([n^c]\), \([n^c]+1\). (English) Zbl 1417.11145 JP J. Algebra Number Theory Appl. 40, No. 6, 945-956 (2018). MSC: 11N25 PDF BibTeX XML Cite \textit{S. I. Dimitrov}, JP J. Algebra Number Theory Appl. 40, No. 6, 945--956 (2018; Zbl 1417.11145) Full Text: DOI
Alweiss, Ryan; Luo, Sammy Bounded gaps between primes in short intervals. (English) Zbl 1441.11239 Res. Number Theory 4, No. 2, Paper No. 15, 27 p. (2018). MSC: 11N05 11N56 11N25 PDF BibTeX XML Cite \textit{R. Alweiss} and \textit{S. Luo}, Res. Number Theory 4, No. 2, Paper No. 15, 27 p. (2018; Zbl 1441.11239) Full Text: DOI
Rome, Nick The Hasse norm principle for biquadratic extensions. (English. French summary) Zbl 1441.11245 J. Théor. Nombres Bordx. 30, No. 3, 947-964 (2018). MSC: 11N25 11R16 PDF BibTeX XML Cite \textit{N. Rome}, J. Théor. Nombres Bordx. 30, No. 3, 947--964 (2018; Zbl 1441.11245) Full Text: DOI arXiv
Guo, Victor Z.; Weingartner, Andreas The practicality of shifted primes. (English) Zbl 1444.11193 Integers 18, Paper A93, 7 p. (2018). MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{V. Z. Guo} and \textit{A. Weingartner}, Integers 18, Paper A93, 7 p. (2018; Zbl 1444.11193) Full Text: Link
Mercer, Idris Dirichlet’s theorem and Jacobsthal’s function. (English) Zbl 1441.11020 Integers 18, Paper A26, 8 p. (2018). MSC: 11B25 11N25 PDF BibTeX XML Cite \textit{I. Mercer}, Integers 18, Paper A26, 8 p. (2018; Zbl 1441.11020) Full Text: Link arXiv
Chan, Tsz Ho Numbers with three close factorizations and lattice points on hyperbolas. (English) Zbl 1425.11158 Integers 18, Paper A13, 9 p. (2018). Reviewer: Amin Witno (Amman) MSC: 11N25 PDF BibTeX XML Cite \textit{T. H. Chan}, Integers 18, Paper A13, 9 p. (2018; Zbl 1425.11158) Full Text: Link
Sokvári, Olivér Patterns of \(k\)th power-free numbers. (English) Zbl 1438.11126 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 61, 93-99 (2018). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 11N25 11B05 11B83 PDF BibTeX XML Cite \textit{O. Sokvári}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 61, 93--99 (2018; Zbl 1438.11126)
Conant, Gabriel Multiplicative structure in stable expansions of the group of integers. (English) Zbl 07036790 Ill. J. Math. 62, No. 1-4, 341-364 (2018). MSC: 03C45 03C60 11N25 11U09 PDF BibTeX XML Cite \textit{G. Conant}, Ill. J. Math. 62, No. 1--4, 341--364 (2018; Zbl 07036790) Full Text: DOI Euclid arXiv
Halupczok, Karin Vinogradov’s mean value theorem as an ingredient in polynomial large sieve inequalities and some consequences. (English) Zbl 1441.11250 Pintz, János (ed.) et al., Irregularities in the distribution of prime numbers. From the era of Helmut Maier’s matrix method and beyond. Cham: Springer. 97-109 (2018). MSC: 11N35 11N25 PDF BibTeX XML Cite \textit{K. Halupczok}, in: Irregularities in the distribution of prime numbers. From the era of Helmut Maier's matrix method and beyond. Cham: Springer. 97--109 (2018; Zbl 1441.11250) Full Text: DOI
Funkhouser, Scott; Goldston, Daniel A.; Ledoan, Andrew H. Distribution of large gaps between primes. (English) Zbl 1441.11241 Pintz, János (ed.) et al., Irregularities in the distribution of prime numbers. From the era of Helmut Maier’s matrix method and beyond. Cham: Springer. 45-67 (2018). MSC: 11N05 11N25 PDF BibTeX XML Cite \textit{S. Funkhouser} et al., in: Irregularities in the distribution of prime numbers. From the era of Helmut Maier's matrix method and beyond. Cham: Springer. 45--67 (2018; Zbl 1441.11241) Full Text: DOI arXiv
Freiberg, Tristan A note on the distribution of primes in intervals. (English) Zbl 1441.11240 Pintz, János (ed.) et al., Irregularities in the distribution of prime numbers. From the era of Helmut Maier’s matrix method and beyond. Cham: Springer. 23-44 (2018). MSC: 11N05 11N25 PDF BibTeX XML Cite \textit{T. Freiberg}, in: Irregularities in the distribution of prime numbers. From the era of Helmut Maier's matrix method and beyond. Cham: Springer. 23--44 (2018; Zbl 1441.11240) Full Text: DOI
Ford, Kevin; Maynard, James; Tao, Terence Chains of large gaps between primes. (English) Zbl 07035248 Pintz, János (ed.) et al., Irregularities in the distribution of prime numbers. From the era of Helmut Maier’s matrix method and beyond. Cham: Springer (ISBN 978-3-319-92776-3/hbk; 978-3-319-92777-0/ebook). 1-21 (2018). Reviewer: Stephan Baier (Haora) MSC: 11N05 11N25 PDF BibTeX XML Cite \textit{K. Ford} et al., in: Irregularities in the distribution of prime numbers. From the era of Helmut Maier's matrix method and beyond. Cham: Springer. 1--21 (2018; Zbl 07035248) Full Text: DOI arXiv
Dubickas, Artūras; Sha, Min Multiplicative dependence of the translations of algebraic numbers. (English) Zbl 1423.11166 Rev. Mat. Iberoam. 34, No. 4, 1789-1808 (2018). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11R04 11D61 PDF BibTeX XML Cite \textit{A. Dubickas} and \textit{M. Sha}, Rev. Mat. Iberoam. 34, No. 4, 1789--1808 (2018; Zbl 1423.11166) Full Text: DOI arXiv
Ledoan, A. H. The discrepancy of Farey series. (English) Zbl 1424.11108 Acta Math. Hung. 156, No. 2, 465-480 (2018). MSC: 11K38 11B57 11N25 PDF BibTeX XML Cite \textit{A. H. Ledoan}, Acta Math. Hung. 156, No. 2, 465--480 (2018; Zbl 1424.11108) Full Text: DOI