Rakhmonov, Zarullo Khusenovich Generalization of Waring’s problem for nine almost proportional cubes. (Russian. English summary) Zbl 07815802 Chebyshevskiĭ Sb. 24, No. 3(89), 71-94 (2023). MSC: 11P05 11P55 11L07 PDFBibTeX XMLCite \textit{Z. K. Rakhmonov}, Chebyshevskiĭ Sb. 24, No. 3(89), 71--94 (2023; Zbl 07815802) Full Text: DOI MNR
Blomer, Valentin (ed.); Einsiedler, Manfred (ed.); Kowalski, Emmanuel (ed.); Viazovska, Maryna (ed.) Group actions and harmonic analysis in number theory. Abstracts from the workshop held May 7–12, 2023. (English) Zbl 1528.11001 Oberwolfach Rep. 20, No. 2, 1195-1262 (2023). MSC: 11-06 00B05 00B25 11Fxx 11Mxx 11T23 22Exx 37A17 42Axx PDFBibTeX XMLCite \textit{V. Blomer} (ed.) et al., Oberwolfach Rep. 20, No. 2, 1195--1262 (2023; Zbl 1528.11001) Full Text: DOI
Brüdern, Jörg; Wooley, Trevor D. On Waring’s problem for larger powers. (English) Zbl 07771193 J. Reine Angew. Math. 805, 115-142 (2023). Reviewer: Mehdi Hassani (Zanjan) MSC: 11P05 11P55 11J71 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, J. Reine Angew. Math. 805, 115--142 (2023; Zbl 07771193) Full Text: DOI arXiv
Mirek, Jarosław; Słomian, Wojciech; Wróbel, Błażej On the solution of Waring problem with a multiplicative error term: dimension-free estimates. (English) Zbl 07688421 Proc. Am. Math. Soc. 151, No. 8, 3365-3379 (2023). Reviewer: Victor Wang (Princeton) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Mirek} et al., Proc. Am. Math. Soc. 151, No. 8, 3365--3379 (2023; Zbl 07688421) Full Text: DOI arXiv
Matomäki, Kaisa (ed.); Soundararajan, Kannan (ed.); Vaughan, Robert C. (ed.); Wooley, Trevor D. (ed.) Analytic number theory. Abstracts from the workshop held November 6–12, 2022. (English) Zbl 1521.00022 Oberwolfach Rep. 19, No. 4, 2895-2960 (2022). MSC: 00B05 00B25 11-06 11Bxx 11Dxx 11Jxx 11Pxx PDFBibTeX XMLCite \textit{K. Matomäki} (ed.) et al., Oberwolfach Rep. 19, No. 4, 2895--2960 (2022; Zbl 1521.00022) Full Text: DOI
Pliego, Javier On Waring’s problem in sums of three cubes. (English) Zbl 1523.11176 Mathematika 67, No. 1, 235-256 (2021). MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Pliego}, Mathematika 67, No. 1, 235--256 (2021; Zbl 1523.11176) Full Text: DOI arXiv
Liu, Jianya; Zhao, Lilu Representation by sums of unlike powers. (English) Zbl 1487.11089 J. Reine Angew. Math. 781, 19-55 (2021). Reviewer: Luis Gallardo (Brest) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Liu} and \textit{L. Zhao}, J. Reine Angew. Math. 781, 19--55 (2021; Zbl 1487.11089) Full Text: DOI arXiv
Chow, Sam; Lindqvist, Sofia; Prendiville, Sean Rado’s criterion over squares and higher powers. (English) Zbl 1497.11028 J. Eur. Math. Soc. (JEMS) 23, No. 6, 1925-1997 (2021). Reviewer: Kaisa Matomäki (Turku) MSC: 11B30 11D72 PDFBibTeX XMLCite \textit{S. Chow} et al., J. Eur. Math. Soc. (JEMS) 23, No. 6, 1925--1997 (2021; Zbl 1497.11028) Full Text: DOI arXiv
Guo, Shaoming; Zhang, Ruixiang On integer solutions of Parsell-Vinogradov systems. (English) Zbl 1447.11090 Invent. Math. 218, No. 1, 1-81 (2019). Reviewer: Huaning Liu (Xi’an) MSC: 11L07 42A45 PDFBibTeX XMLCite \textit{S. Guo} and \textit{R. Zhang}, Invent. Math. 218, No. 1, 1--81 (2019; Zbl 1447.11090) Full Text: DOI arXiv
Kuo, Wentang; Liu, Yu-Ru; Zhao, Xiaomei The asymptotic estimates and Hasse principle for multidimensional Waring’s problem. (English) Zbl 1442.11137 Adv. Math. 353, 1-66 (2019). Reviewer: D. R. Heath-Brown (Garsington) MSC: 11P05 11P55 11T55 PDFBibTeX XMLCite \textit{W. Kuo} et al., Adv. Math. 353, 1--66 (2019; Zbl 1442.11137) Full Text: DOI
Bell, Jason; Hare, Kathryn; Shallit, Jeffrey When is an automatic set an additive basis? (English) Zbl 1437.11017 Proc. Am. Math. Soc., Ser. B 5, 50-63 (2018). MSC: 11B13 11B85 68Q45 28A80 PDFBibTeX XMLCite \textit{J. Bell} et al., Proc. Am. Math. Soc., Ser. B 5, 50--63 (2018; Zbl 1437.11017) Full Text: DOI arXiv
Zhao, Lilu Rational lines on cubic hypersurfaces. (English) Zbl 1375.11066 Isr. J. Math. 215, No. 2, 877-907 (2016). Reviewer: Mihály Szalay (Budapest) MSC: 11P05 11L07 11D45 11D25 11D72 11P55 PDFBibTeX XMLCite \textit{L. Zhao}, Isr. J. Math. 215, No. 2, 877--907 (2016; Zbl 1375.11066) Full Text: DOI
Drappeau, Sary; Shao, Xuancheng Weyl sums, mean value estimates, and Waring’s problem with friable numbers. (English) Zbl 1385.11052 Acta Arith. 176, No. 3, 249-299 (2016). Reviewer: Ram Krishna Pandey (Roorkee) MSC: 11L07 11P05 11N25 PDFBibTeX XMLCite \textit{S. Drappeau} and \textit{X. Shao}, Acta Arith. 176, No. 3, 249--299 (2016; Zbl 1385.11052) Full Text: DOI arXiv
Brüdern, Jörg; Dietmann, Rainer Random Diophantine equations. I. (English) Zbl 1356.11016 Adv. Math. 256, 18-45 (2014). MSC: 11D72 11E76 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{R. Dietmann}, Adv. Math. 256, 18--45 (2014; Zbl 1356.11016) Full Text: DOI arXiv
Hayman, W. K. Waring’s theorem and the super Fermat problem for numbers and functions. (English) Zbl 1306.11081 Complex Var. Elliptic Equ. 59, No. 1, 85-90 (2014). Reviewer: Luis Gallardo (Brest) MSC: 11P05 30D35 11D41 PDFBibTeX XMLCite \textit{W. K. Hayman}, Complex Var. Elliptic Equ. 59, No. 1, 85--90 (2014; Zbl 1306.11081) Full Text: DOI
Parsell, Scott T. Hua-type iteration for multidimensional Weyl sums. (English) Zbl 1284.11059 Mathematika 58, No. 2, 209-224 (2012). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11D45 11P55 11L15 11D72 PDFBibTeX XMLCite \textit{S. T. Parsell}, Mathematika 58, No. 2, 209--224 (2012; Zbl 1284.11059) Full Text: DOI
Wooley, Trevor D. Vinogradov’s mean value theorem via efficient congruencing. (English) Zbl 1267.11105 Ann. Math. (2) 175, No. 3, 1575-1627 (2012). Reviewer: Stephan Baier (Norwich) MSC: 11P05 11P55 11L07 PDFBibTeX XMLCite \textit{T. D. Wooley}, Ann. Math. (2) 175, No. 3, 1575--1627 (2012; Zbl 1267.11105) Full Text: DOI arXiv
Liu, Yu-Ru; Wooley, Trevor D. Waring’s problem in function fields. (English) Zbl 1221.11203 J. Reine Angew. Math. 638, 1-67 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11P05 11T55 11P55 PDFBibTeX XMLCite \textit{Y.-R. Liu} and \textit{T. D. Wooley}, J. Reine Angew. Math. 638, 1--67 (2010; Zbl 1221.11203) Full Text: DOI
Parsell, Scott T. Asymptotic estimates for rational linear spaces on hypersurfaces. (English) Zbl 1181.11035 Trans. Am. Math. Soc. 361, No. 6, 2929-2957 (2009). Reviewer: B. Z. Moroz (Bonn) MSC: 11D45 11D72 11L07 11P55 14J70 11D41 PDFBibTeX XMLCite \textit{S. T. Parsell}, Trans. Am. Math. Soc. 361, No. 6, 2929--2957 (2009; Zbl 1181.11035) Full Text: DOI
Gallardo, Luis H.; Vaserstein, Leonid N. The strict Waring problem for polynomial rings. (English) Zbl 1220.11151 J. Number Theory 128, No. 12, 2963-2972 (2008). Reviewer: Florin Nicolae (Berlin) MSC: 11T55 11D85 11P05 PDFBibTeX XMLCite \textit{L. H. Gallardo} and \textit{L. N. Vaserstein}, J. Number Theory 128, No. 12, 2963--2972 (2008; Zbl 1220.11151) Full Text: DOI
Thuswaldner, Jörg M.; Tichy, Robert F. Waring’s problem with digital restrictions. (English) Zbl 1132.11050 Isr. J. Math. 149, 317-344 (2005). MSC: 11P05 PDFBibTeX XMLCite \textit{J. M. Thuswaldner} and \textit{R. F. Tichy}, Isr. J. Math. 149, 317--344 (2005; Zbl 1132.11050) Full Text: DOI
Nesterenko, Yu. V. On Waring’s problem (elementary methods). (English, Russian) Zbl 1072.11073 J. Math. Sci., New York 137, No. 2, 4699-4715 (2006); translation from Zap. Nauchn. Semin. POMI 322, 149-175 (2005). Reviewer: L. N. Vaserstein (University Park) MSC: 11P05 PDFBibTeX XMLCite \textit{Yu. V. Nesterenko}, J. Math. Sci., New York 137, No. 2, 149--175 (2005; Zbl 1072.11073); translation from Zap. Nauchn. Semin. POMI 322, 149--175 (2005) Full Text: DOI EuDML
Vaserstein, L. N.; Wheland, E. R. Vanishing polynomial sums. (English) Zbl 1073.12001 Commun. Algebra 31, No. 2, 751-772 (2003). Reviewer: Leonardo Cangelmi (Pescara) MSC: 12E05 11D41 PDFBibTeX XMLCite \textit{L. N. Vaserstein} and \textit{E. R. Wheland}, Commun. Algebra 31, No. 2, 751--772 (2003; Zbl 1073.12001) Full Text: DOI
Laporta, M. B. S.; Wooley, T. D. The representation of almost all numbers as sums of unlike powers. (English) Zbl 1048.11074 J. Théor. Nombres Bordx. 13, No. 1, 227-240 (2001). Reviewer: Koichi Kawada (Morioka) MSC: 11P05 11P55 11L15 PDFBibTeX XMLCite \textit{M. B. S. Laporta} and \textit{T. D. Wooley}, J. Théor. Nombres Bordx. 13, No. 1, 227--240 (2001; Zbl 1048.11074) Full Text: DOI Numdam EuDML EMIS
Brüdern, Jörg; Wooley, Trevor D. On Waring’s problem: Three cubes and a sixth power. (English) Zbl 0989.11047 Nagoya Math. J. 163, 13-53 (2001). Reviewer: Roger Heath-Brown (Oxford) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, Nagoya Math. J. 163, 13--53 (2001; Zbl 0989.11047) Full Text: DOI
Brüdern, Jörg; Kawada, Koichi; Wooley, Trevor D. Additive representation in thin sequences. I: Waring’s problem for cubes. (English) Zbl 1020.11062 Ann. Sci. Éc. Norm. Supér. (4) 34, No. 4, 471-501 (2001). Reviewer: George Greaves (Cardiff) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} et al., Ann. Sci. Éc. Norm. Supér. (4) 34, No. 4, 471--501 (2001; Zbl 1020.11062) Full Text: DOI Numdam EuDML
Brüdern, J.; Kawada, K.; Wooley, T. D. Additive representation in thin sequences. II: The binary Goldbach problem. (English) Zbl 1023.11053 Mathematika 47, No. 1-2, 117-125 (2000). Reviewer: George Greaves (Cardiff) MSC: 11P32 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} et al., Mathematika 47, No. 1--2, 117--125 (2000; Zbl 1023.11053) Full Text: DOI
Wooley, Trevor D. On simultaneous additive equations. IV. (English) Zbl 0994.11015 Mathematika 45, No. 2, 319-335 (1998). Reviewer: Koichi Kawada (Morioka) MSC: 11D72 11L15 11P55 11D25 PDFBibTeX XMLCite \textit{T. D. Wooley}, Mathematika 45, No. 2, 319--335 (1998; Zbl 0994.11015) Full Text: DOI
Davidson, Morley Sums of \(k\)-th powers in number fields. (English) Zbl 0995.11056 Mathematika 45, No. 2, 359-370 (1998). Reviewer: L.N.Vaserstein (University Park) MSC: 11P05 11R99 11P55 PDFBibTeX XMLCite \textit{M. Davidson}, Mathematika 45, No. 2, 359--370 (1998; Zbl 0995.11056) Full Text: DOI
Ford, Kevin B. The representation of numbers as sums of unlike powers. II. (English) Zbl 0866.11054 J. Am. Math. Soc. 9, No. 4, 919-940 (1996); addendum and corrigendum ibid. 12, No. 4, 1213 (1999). Reviewer: M.-C.Liu (Hongkong) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{K. B. Ford}, J. Am. Math. Soc. 9, No. 4, 919--940 (1996; Zbl 0866.11054) Full Text: DOI
Meng, Zaizhao Some new results in Waring’s problem. (English) Zbl 0923.11139 Acta Math. Sin., New Ser. 12, No. 3, 262-267 (1996). Reviewer: Ming-Chit Liu (Hongkong) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{Z. Meng}, Acta Math. Sin., New Ser. 12, No. 3, 262--267 (1996; Zbl 0923.11139) Full Text: DOI
Wooley, Trevor D. Some remarks on Vinogradov’s mean value theorem and Tarry’s problem. (English) Zbl 0881.11043 Monatsh. Math. 122, No. 3, 265-273 (1996). Reviewer: Ming-Chit Liu (Hongkong) MSC: 11D72 11D45 11P05 11P55 11L07 PDFBibTeX XMLCite \textit{T. D. Wooley}, Monatsh. Math. 122, No. 3, 265--273 (1996; Zbl 0881.11043) Full Text: DOI EuDML
Kawada, Koichi On the sum of four cubes. (English) Zbl 0879.11051 Mathematika 43, No. 2, 323-348 (1996). Reviewer: G.Greaves (Cardiff) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{K. Kawada}, Mathematika 43, No. 2, 323--348 (1996; Zbl 0879.11051) Full Text: DOI
Wooley, Trevor D. Breaking classical convexity in Waring’s problem: sums of cubes and quasi-diagonal behaviour. (English) Zbl 0851.11055 Invent. Math. 122, No. 3, 421-451 (1995). Reviewer: George Greaves (Cardiff) MSC: 11P05 PDFBibTeX XMLCite \textit{T. D. Wooley}, Invent. Math. 122, No. 3, 421--451 (1995; Zbl 0851.11055) Full Text: DOI EuDML
Vaughan, Robert C.; Wooley, Trevor D. Further improvements in Waring’s problem. (English) Zbl 0849.11075 Acta Math. 174, No. 2, 147-240 (1995). MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{R. C. Vaughan} and \textit{T. D. Wooley}, Acta Math. 174, No. 2, 147--240 (1995; Zbl 0849.11075) Full Text: DOI
Brüdern, Jörg; Watt, Nigel On Waring’s problem for four cubes. (English) Zbl 0828.11051 Duke Math. J. 77, No. 3, 583-606 (1995). Reviewer: G.Greaves (Cardiff) MSC: 11P05 11P55 11L15 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{N. Watt}, Duke Math. J. 77, No. 3, 583--606 (1995; Zbl 0828.11051) Full Text: DOI
Li, Hongze The solubility of certain diophantine inequalities. (English) Zbl 0828.11017 Acta Math. Sin., New Ser. 11, No. 2, 137-145 (1995). Reviewer: M.-C.Liu (Hongkong) MSC: 11D75 11J25 PDFBibTeX XMLCite \textit{H. Li}, Acta Math. Sin., New Ser. 11, No. 2, 137--145 (1995; Zbl 0828.11017) Full Text: DOI
Vaughan, R. C.; Wooley, T. D. Further improvements in Waring’s problem. II: Sixth powers. (English) Zbl 0849.11076 Duke Math. J. 76, No. 3, 683-710 (1994). MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{R. C. Vaughan} and \textit{T. D. Wooley}, Duke Math. J. 76, No. 3, 683--710 (1994; Zbl 0849.11076) Full Text: DOI
Wooley, Trevor D. Quasi-diagonal behaviour in certain mean value theorems of additive number theory. (English) Zbl 0786.11053 J. Am. Math. Soc. 7, No. 1, 221-245 (1994). Reviewer: E.Krätzel (Jena) MSC: 11L15 11P05 PDFBibTeX XMLCite \textit{T. D. Wooley}, J. Am. Math. Soc. 7, No. 1, 221--245 (1994; Zbl 0786.11053) Full Text: DOI
Hildebrand, Adolf; Tenenbaum, Gérald Integers without large prime factors. (English) Zbl 0797.11070 J. Théor. Nombres Bordx. 5, No. 2, 411-484 (1993). Reviewer: Andrew Granville (Athens/Georgia) MSC: 11N25 11-02 PDFBibTeX XMLCite \textit{A. Hildebrand} and \textit{G. Tenenbaum}, J. Théor. Nombres Bordx. 5, No. 2, 411--484 (1993; Zbl 0797.11070) Full Text: DOI Numdam EuDML
Wooley, Trevor D. On Vinogradov’s mean value theorem. (English) Zbl 0769.11036 Mathematika 39, No. 2, 379-399 (1992). Reviewer: J.Brüdern (Göttingen) MSC: 11P05 11D72 PDFBibTeX XMLCite \textit{T. D. Wooley}, Mathematika 39, No. 2, 379--399 (1992; Zbl 0769.11036) Full Text: DOI