Perret-Gentil, Corentin Roots of \(L\)-functions of characters over function fields, generic linear independence and biases. (English) Zbl 07244795 Algebra Number Theory 14, No. 5, 1291-1329 (2020). MSC: 11J72 11N36 11R58 11T23 PDF BibTeX XML Cite \textit{C. Perret-Gentil}, Algebra Number Theory 14, No. 5, 1291--1329 (2020; Zbl 07244795) Full Text: DOI
Mukhopadhyay, Madhurima; Sarkar, Palash Faster initial splitting for small characteristic composite extension degree fields. (English) Zbl 07174361 Finite Fields Appl. 62, Article ID 101629, 16 p. (2020). MSC: 11T71 11Y16 94A60 12E20 11N35 PDF BibTeX XML Cite \textit{M. Mukhopadhyay} and \textit{P. Sarkar}, Finite Fields Appl. 62, Article ID 101629, 16 p. (2020; Zbl 07174361) Full Text: DOI
Guillevic, Aurore Faster individual discrete logarithms in finite fields of composite extension degree. (English) Zbl 07009722 Math. Comput. 88, No. 317, 1273-1301 (2019). MSC: 11T71 94A60 11Y16 PDF BibTeX XML Cite \textit{A. Guillevic}, Math. Comput. 88, No. 317, 1273--1301 (2019; Zbl 07009722) Full Text: DOI
Baier, S.; Bansal, A.; Singh, R. Kumar Divisibility problems for function fields. (English) Zbl 1424.11064 Acta Math. Hung. 156, No. 2, 435-448 (2018); corrigendum ibid. 160, No. 2, 519-521 (2020). MSC: 11B75 11N36 11L40 11P99 PDF BibTeX XML Cite \textit{S. Baier} et al., Acta Math. Hung. 156, No. 2, 435--448 (2018; Zbl 1424.11064) Full Text: DOI
Granger, Robert; Kleinjung, Thorsten; Zumbrägel, Jens Indiscreet logarithms in finite fields of small characteristic. (English) Zbl 1414.11166 Adv. Math. Commun. 12, No. 2, 263-286 (2018). MSC: 11Y16 11T71 94A60 PDF BibTeX XML Cite \textit{R. Granger} et al., Adv. Math. Commun. 12, No. 2, 263--286 (2018; Zbl 1414.11166) Full Text: DOI
Barbulescu, Razvan; Lachand, Armand Some mathematical remarks on the polynomial selection in NFS. (English) Zbl 1359.11031 Math. Comput. 86, No. 303, 397-418 (2017). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11E76 11N25 11N36 11Y05 11Y16 PDF BibTeX XML Cite \textit{R. Barbulescu} and \textit{A. Lachand}, Math. Comput. 86, No. 303, 397--418 (2017; Zbl 1359.11031) Full Text: DOI
Castillo, Abel; Hall, Chris; Lemke Oliver, Robert J.; Pollack, Paul; Thompson, Lola Bounded gaps between primes in number fields and function fields. (English) Zbl 1321.11098 Proc. Am. Math. Soc. 143, No. 7, 2841-2856 (2015). Reviewer: Giovanni Coppola (Avellino) MSC: 11N05 11N36 11T06 PDF BibTeX XML Cite \textit{A. Castillo} et al., Proc. Am. Math. Soc. 143, No. 7, 2841--2856 (2015; Zbl 1321.11098) Full Text: DOI arXiv
Watt, Nigel Weighted fourth moments of Hecke zeta functions with groessencharacters. (English) Zbl 1357.11086 Mosc. J. Comb. Number Theory 4, No. 2, 3-118 (2014). MSC: 11M41 11F30 11F37 11F72 11L05 PDF BibTeX XML Cite \textit{N. Watt}, Mosc. J. Comb. Number Theory 4, No. 2, 3--118 (2014; Zbl 1357.11086) Full Text: arXiv
Barbulescu, Razvan; Bouvier, Cyril; Detrey, Jérémie; Gaudry, Pierrick; Jeljeli, Hamza; Thomé, Emmanuel; Videau, Marion; Zimmermann, Paul Discrete logarithm in \(\mathrm{GF}(2^{809})\) with FFS. (English) Zbl 1335.94029 Krawczyk, Hugo (ed.), Public-key cryptography – PKC 2014. 17th international conference on practice and theory in public-key cryptography, Buenos Aires, Argentina, March 26–28, 2014. Proceedings. Berlin: Springer (ISBN 978-3-642-54630-3/pbk). Lecture Notes in Computer Science 8383, 221-238 (2014). MSC: 94A60 11Y16 11T71 PDF BibTeX XML Cite \textit{R. Barbulescu} et al., Lect. Notes Comput. Sci. 8383, 221--238 (2014; Zbl 1335.94029) Full Text: DOI
Tamam, Nattalie The fourth moment of Dirichlet \(L\)-functions for the rational function field. (English) Zbl 1329.11095 Int. J. Number Theory 10, No. 1, 183-218 (2014). MSC: 11M38 11N36 11T06 PDF BibTeX XML Cite \textit{N. Tamam}, Int. J. Number Theory 10, No. 1, 183--218 (2014; Zbl 1329.11095) Full Text: DOI arXiv
Göloğlu, Faruk; Granger, Robert; McGuire, Gary; Zumbrägel, Jens On the function field sieve and the impact of higher splitting probabilities. Application to discrete logarithms in \(\mathbb{F}_{2^{1971}}\) and \(\mathbb{F}_{2^{3164}}\). (English) Zbl 1316.11114 Canetti, Ran (ed.) et al., Advances in cryptology – CRYPTO 2013. 33rd annual cryptology conference, Santa Barbara, CA, USA, August 18–22, 2013. Proceedings, Part II. Berlin: Springer (ISBN 978-3-642-40083-4/pbk). Lecture Notes in Computer Science 8043, 109-128 (2013). MSC: 11Y16 11T71 94A60 PDF BibTeX XML Cite \textit{F. Göloğlu} et al., Lect. Notes Comput. Sci. 8043, 109--128 (2013; Zbl 1316.11114) Full Text: DOI
Hayashi, Takuya; Shimoyama, Takeshi; Shinohara, Naoyuki; Takagi, Tsuyoshi Breaking pairing-based cryptosystems using \(\eta_T\) pairing over \(GF(3^{97})\). (English) Zbl 1292.94073 Wang, Xiaoyun (ed.) et al., Advances in cryptology – ASIACRYPT 2012. 18th international conference on the theory and application of cryptology and information security, Beijing, China, December 2–6, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-34960-7/pbk). Lecture Notes in Computer Science 7658, 43-60 (2012). MSC: 94A60 11Y16 PDF BibTeX XML Cite \textit{T. Hayashi} et al., Lect. Notes Comput. Sci. 7658, 43--60 (2012; Zbl 1292.94073) Full Text: DOI
Riesel, Hans Prime numbers and computer methods for factorization. Reprint of the 2nd ed. 1994. (English) Zbl 1272.11001 Modern Birkhäuser Classics. New York, NY: Birkhäuser/Springer (ISBN 978-0-8176-8297-2/pbk; 978-0-8176-8298-9/ebook). xviii, 464 p. (2012). Reviewer: Olaf Ninnemann (Berlin) MSC: 11-01 11-02 11Yxx 11-04 11Y05 11Y11 11Y16 11N05 11N13 11A41 11A51 68W30 94A60 PDF BibTeX XML Cite \textit{H. Riesel}, Prime numbers and computer methods for factorization. Reprint of the 2nd ed. 1994. New York, NY: Birkhäuser/Springer (2012; Zbl 1272.11001) Full Text: DOI
Hayashi, Takuya; Shinohara, Naoyuki; Wang, Lihua; Matsuo, Shin’ichiro; Shirase, Masaaki; Takagi, Tsuyoshi Solving a 676-bit discrete logarithm problem in \(\text{GF}(3^{6n})\). (English) Zbl 1281.94028 Nguyen, Phong Q. (ed.) et al., Public key cryptography – PKC 2010. 13th international conference on practice and theory in public key cryptography, Paris, France, May 26–28, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-13012-0/pbk). Lecture Notes in Computer Science 6056, 351-367 (2010). MSC: 94A60 11T71 PDF BibTeX XML Cite \textit{T. Hayashi} et al., Lect. Notes Comput. Sci. 6056, 351--367 (2010; Zbl 1281.94028) Full Text: DOI
Schirokauer, Oliver The impact of the number field sieve on the discrete logarithm problem in finite fields. (English) Zbl 1188.11071 Buhler, J. P. (ed.) et al., Algorithmic number theory. Lattices, number fields, curves and cryptography. Cambridge: Cambridge University Press (ISBN 978-0-521-80854-5/hbk). Mathematical Sciences Research Institute Publications 44, 397-420 (2008). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 11Y16 11Y05 94A60 11Y40 11T71 PDF BibTeX XML Cite \textit{O. Schirokauer}, Math. Sci. Res. Inst. Publ. 44, 397--420 (2008; Zbl 1188.11071)
Zhang, Chaogui Distribution of \(k\)-semismooth integers. (English) Zbl 1191.11026 Panam. Math. J. 18, No. 4, 45-60 (2008). Reviewer: Zaizhao Meng (Beijing) MSC: 11N25 PDF BibTeX XML Cite \textit{C. Zhang}, Panam. Math. J. 18, No. 4, 45--60 (2008; Zbl 1191.11026)
Loh, Wei-Liem Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields. (English) Zbl 1086.62111 Ann. Stat. 33, No. 5, 2344-2394 (2005). MSC: 62M40 62G05 62G20 62E20 PDF BibTeX XML Cite \textit{W.-L. Loh}, Ann. Stat. 33, No. 5, 2344--2394 (2005; Zbl 1086.62111) Full Text: DOI arXiv
Granger, R.; Holt, A. J.; Page, D.; Smart, N. P.; Vercauteren, F. Function field sieve in characteristic three. (English) Zbl 1125.11358 Buell, Duncan (ed.), Algorithmic number theory. 6th international symposium, ANTS-VI, Burlington, VT, USA, June 13–18, 2004. Proceedings. Berlin: Springer (ISBN 3-540-22156-5/pbk). Lecture Notes in Computer Science 3076, 223-234 (2004). MSC: 11T71 11Y16 14G50 94A60 PDF BibTeX XML Cite \textit{R. Granger} et al., Lect. Notes Comput. Sci. 3076, 223--234 (2004; Zbl 1125.11358) Full Text: DOI
Bauer, Mark L.; Hamdy, Safuat On class group computations using the number field sieve. (English) Zbl 1205.11138 Laih, Chi Sung (ed.), Advances in cryptology – ASIACRYPT 2003. 9th international conference on the theory and application of cryptology and information security, Taipei, Taiwan, November 30 – December 4, 2003. Proceedings. Berlin: Springer (ISBN 3-540-20592-6/pbk). Lect. Notes Comput. Sci. 2894, 311-325 (2003). MSC: 11Y40 11R29 14G50 94A60 PDF BibTeX XML Cite \textit{M. L. Bauer} and \textit{S. Hamdy}, Lect. Notes Comput. Sci. 2894, 311--325 (2003; Zbl 1205.11138) Full Text: DOI
Schirokauer, Oliver The special function field sieve. (English) Zbl 1040.11097 SIAM J. Discrete Math. 16, No. 1, 81-98 (2002). MSC: 11Y16 11Y40 PDF BibTeX XML Cite \textit{O. Schirokauer}, SIAM J. Discrete Math. 16, No. 1, 81--98 (2002; Zbl 1040.11097) Full Text: DOI
Jensen, Erik; Murty, M. Ram Artin’s conjecture for polynomials over finite fields. (English) Zbl 0987.11074 Bambah, R. P. (ed.) et al., Number theory. Basel: Birkhäuser. Trends in Mathematics. 167-181 (2000). Reviewer: George Greaves (Cardiff) MSC: 11T06 11A07 11N36 PDF BibTeX XML Cite \textit{E. Jensen} and \textit{M. R. Murty}, in: Number theory. Basel: Birkhäuser. 167--181 (2000; Zbl 0987.11074)
Adleman, Leonard M.; Huang, Ming-Deh A. Function field sieve method for discrete logarithms over finite fields. (English) Zbl 1006.11078 Inf. Comput. 151, No. 1-2, 5-16 (1999). MSC: 11Y16 68P25 11T71 PDF BibTeX XML Cite \textit{L. M. Adleman} and \textit{M.-D. A. Huang}, Inf. Comput. 151, No. 1--2, 5--16 (1999; Zbl 1006.11078) Full Text: DOI
Adleman, Leonard M.; Huang, Ming-Deh Function field sieve method for discrete logarithms over finite fields. (English) Zbl 1007.11079 Fried, Michael D. (ed.), Applications of curves over finite fields. 1997 AMS-IMS-SIAM joint summer research conference, July 27-31, 1997, Seattle, WA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 245, 133-143 (1999). MSC: 11Y16 68P25 11T71 PDF BibTeX XML Cite \textit{L. M. Adleman} and \textit{M.-D. Huang}, Contemp. Math. 245, 133--143 (1999; Zbl 1007.11079)
Thuswaldner, Jörg M. The fundamental lemma of Kubilius and the model of Kubilius in number fields. (English) Zbl 0914.11051 Győry, Kálmán (ed.) et al., Number theory. Diophantine, computational and algebraic aspects. Proceedings of the international conference, Eger, Hungary, July 29–August 2, 1996. Berlin: de Gruyter. 489-499 (1998). Reviewer: Wolfgang Schwarz (Frankfurt am Main) MSC: 11N36 11N60 11R04 PDF BibTeX XML Cite \textit{J. M. Thuswaldner}, in: Number theory. Diophantine, computational and algebraic aspects. Proceedings of the international conference, Eger, Hungary, July 29--August 2, 1996. Berlin: de Gruyter. 489--499 (1998; Zbl 0914.11051)
Riesel, Hans Prime numbers and computer methods for factorization. 2nd ed. (English) Zbl 0821.11001 Progress in Mathematics (Boston, Mass.). 126. Boston, MA: Birkhäuser. xvi, 464 p. (1994). Reviewer: A.A.Mullin (Huntsville) MSC: 11-01 11-02 11Yxx 11-04 11Y05 11Y11 11Y16 11N05 11A41 11A51 68Q25 94A60 PDF BibTeX XML Cite \textit{H. Riesel}, Prime numbers and computer methods for factorization. 2nd ed. Boston, MA: Birkhäuser (1994; Zbl 0821.11001)
Nair, Mohan; Perelli, Alberto Sieve methods and class-number problems. I. (English) Zbl 0588.10053 J. Reine Angew. Math. 367, 11-26 (1986). Reviewer: S.Kanemitsu MSC: 11N35 11N05 11R23 11R11 11N37 PDF BibTeX XML Cite \textit{M. Nair} and \textit{A. Perelli}, J. Reine Angew. Math. 367, 11--26 (1986; Zbl 0588.10053) Full Text: Crelle EuDML