Pazuki, Fabien The regulator dominates the rank. (English) Zbl 07660624 Anni, Samuele (ed.) et al., Arithmetic, geometry, cryptography, and coding theory, AGC2T. 18th international conference, Centre International de Rencontres Mathématiques, Marseille, France, May 31 – June 4, 2021. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 779, 159-165 (2022). Reviewer: David McKinnon (Waterloo) MSC: 11G50 14G40 PDF BibTeX XML Cite \textit{F. Pazuki}, Contemp. Math. 779, 159--165 (2022; Zbl 07660624) Full Text: DOI arXiv OpenURL
Gvirtz, Damián; Loughran, Daniel; Nakahara, Masahiro Quantitative arithmetic of diagonal degree 2 \(K3\) surfaces. (English) Zbl 1507.14035 Math. Ann. 384, No. 1-2, 135-209 (2022). Reviewer: Masato Kuwata (Tokyo) MSC: 14G12 14G05 14F22 14J28 PDF BibTeX XML Cite \textit{D. Gvirtz} et al., Math. Ann. 384, No. 1--2, 135--209 (2022; Zbl 1507.14035) Full Text: DOI arXiv OpenURL
Gillibert, Jean; Levin, Aaron Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil rank. (English) Zbl 1490.14024 Algebra Number Theory 16, No. 2, 311-333 (2022). Reviewer: Nathan Grieve (Kingston) MSC: 14D10 14G25 14K15 PDF BibTeX XML Cite \textit{J. Gillibert} and \textit{A. Levin}, Algebra Number Theory 16, No. 2, 311--333 (2022; Zbl 1490.14024) Full Text: DOI arXiv OpenURL
Gvirtz, Damián; Skorobogatov, Alexei N. Cohomology and the Brauer groups of diagonal surfaces. (English) Zbl 1503.14022 Duke Math. J. 171, No. 6, 1299-1347 (2022). Reviewer: G. K. Sankaran (Bath) MSC: 14F22 14Q10 PDF BibTeX XML Cite \textit{D. Gvirtz} and \textit{A. N. Skorobogatov}, Duke Math. J. 171, No. 6, 1299--1347 (2022; Zbl 1503.14022) Full Text: DOI arXiv OpenURL
Leterrier, Gauthier On the Mordell-Weil lattice of \(y^2=x^3+bx+t^{3^n+1}\) in characteristic 3. (English) Zbl 1495.11072 Res. Number Theory 8, No. 2, Paper No. 23, 20 p. (2022). Reviewer: Mohammad Sadek (New Cairo) MSC: 11G05 11M38 11T24 52C15 PDF BibTeX XML Cite \textit{G. Leterrier}, Res. Number Theory 8, No. 2, Paper No. 23, 20 p. (2022; Zbl 1495.11072) Full Text: DOI arXiv OpenURL
Lai, King-Fai; Longhi, Ignazio; Suzuki, Takashi; Tan, Ki-Seng; Trihan, Fabien On the \(\mu\)-invariants of abelian varieties over function fields of positive characteristic. (English) Zbl 1479.11191 Algebra Number Theory 15, No. 4, 863-907 (2021). MSC: 11R23 11G10 11S40 14J27 PDF BibTeX XML Cite \textit{K.-F. Lai} et al., Algebra Number Theory 15, No. 4, 863--907 (2021; Zbl 1479.11191) Full Text: DOI arXiv Link OpenURL
Wawrów, Wojciech On torsion of superelliptic Jacobians. (English. French summary) Zbl 1475.14054 J. Théor. Nombres Bordx. 33, No. 1, 223-235 (2021). MSC: 14H40 14G10 14H45 PDF BibTeX XML Cite \textit{W. Wawrów}, J. Théor. Nombres Bordx. 33, No. 1, 223--235 (2021; Zbl 1475.14054) Full Text: DOI arXiv OpenURL
Salami, Sajad Twists of the Albanese varieties of cyclic multiple planes with large ranks over higher dimension function fields. (English. French summary) Zbl 1470.11164 J. Théor. Nombres Bordx. 32, No. 3, 861-876 (2020). Reviewer: Alejandro José Giangreco Maidana (Asunción) MSC: 11G10 14H40 14H05 PDF BibTeX XML Cite \textit{S. Salami}, J. Théor. Nombres Bordx. 32, No. 3, 861--876 (2020; Zbl 1470.11164) Full Text: DOI arXiv OpenURL
Berger, Lisa; Hall, Chris; Pannekoek, René; Park, Jennifer; Pries, Rachel; Sharif, Shahed; Silverberg, Alice; Ulmer, Douglas Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields. (English) Zbl 1465.11002 Memoirs of the American Mathematical Society 1295. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4219-4/pbk; 978-1-4704-6253-6/ebook). v, 131 p. (2020). Reviewer: Ahmed Lesfari (El Jadida) MSC: 11-02 11G05 11G40 11G30 14H05 PDF BibTeX XML Cite \textit{L. Berger} et al., Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields. Providence, RI: American Mathematical Society (AMS) (2020; Zbl 1465.11002) Full Text: DOI arXiv OpenURL
Conceição, Ricardo On integral points on isotrivial elliptic curves over function fields. (English) Zbl 1456.11102 Bull. Aust. Math. Soc. 102, No. 2, 177-185 (2020). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 11G20 PDF BibTeX XML Cite \textit{R. Conceição}, Bull. Aust. Math. Soc. 102, No. 2, 177--185 (2020; Zbl 1456.11102) Full Text: DOI arXiv OpenURL
Griffon, Richard; Ulmer, Douglas On the arithmetic of a family of twisted constant elliptic curves. (English) Zbl 1458.11093 Pac. J. Math. 305, No. 2, 597-640 (2020). Reviewer: Ernst-Ulrich Gekeler (Saarbrücken) MSC: 11G05 14J27 11G40 11G99 14G10 14G99 PDF BibTeX XML Cite \textit{R. Griffon} and \textit{D. Ulmer}, Pac. J. Math. 305, No. 2, 597--640 (2020; Zbl 1458.11093) Full Text: DOI arXiv Link OpenURL
Gong, Cheng; Xu, Wan-Yuan On the Mordell-Weil rank of a surface fibration. (English) Zbl 1440.14049 Commun. Algebra 48, No. 2, 724-732 (2020). MSC: 14D06 14G05 14H05 PDF BibTeX XML Cite \textit{C. Gong} and \textit{W.-Y. Xu}, Commun. Algebra 48, No. 2, 724--732 (2020; Zbl 1440.14049) Full Text: DOI OpenURL
Gorchinskiy, S. O.; Kulikov, Vik. S.; Parshin, A. N.; Popov, V. L. Igor Rostislavovich Shafarevich and his mathematical heritage. (English. Russian original) Zbl 1440.01025 Proc. Steklov Inst. Math. 307, 1-21 (2019); translation from Tr. Mat. Inst. Steklova 307, 9-31 (2019). MSC: 01A70 11-03 14-03 20-03 PDF BibTeX XML Cite \textit{S. O. Gorchinskiy} et al., Proc. Steklov Inst. Math. 307, 1--21 (2019; Zbl 1440.01025); translation from Tr. Mat. Inst. Steklova 307, 9--31 (2019) Full Text: DOI OpenURL
Gillibert, Jean; Levin, Aaron Elliptic surfaces over \(\mathbb P^1\) and large class groups of number fields. (English) Zbl 1439.11279 Int. J. Number Theory 15, No. 10, 2151-2162 (2019). Reviewer: Nathan Kaplan (Irvine) MSC: 11R29 11G05 14J27 PDF BibTeX XML Cite \textit{J. Gillibert} and \textit{A. Levin}, Int. J. Number Theory 15, No. 10, 2151--2162 (2019; Zbl 1439.11279) Full Text: DOI arXiv OpenURL
Hindry, Marc Analogues of Brauer-Siegel theorem in arithmetic geometry. (English) Zbl 1443.11237 Aubry, Yves (ed.) et al., Arithmetic geometry: computation and applications. 16th international conference on arithmetic, geometry, cryptography, and coding theory, AGC2T, CIRM, Marseille, France, June 19–23, 2017. Proceedings. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 722, 19-41 (2019). MSC: 11R42 11R29 14F22 14G10 PDF BibTeX XML Cite \textit{M. Hindry}, Contemp. Math. 722, 19--41 (2019; Zbl 1443.11237) Full Text: DOI Link OpenURL
Park, Jennifer; Poonen, Bjorn; Voight, John; Wood, Melanie Matchett A heuristic for boundedness of ranks of elliptic curves. (English) Zbl 1469.11173 J. Eur. Math. Soc. (JEMS) 21, No. 9, 2859-2903 (2019). MSC: 11G05 11G40 11P21 14G25 PDF BibTeX XML Cite \textit{J. Park} et al., J. Eur. Math. Soc. (JEMS) 21, No. 9, 2859--2903 (2019; Zbl 1469.11173) Full Text: DOI arXiv OpenURL
Ulmer, Douglas On the Brauer-Siegel ratio for abelian varieties over function fields. (English) Zbl 1482.11083 Algebra Number Theory 13, No. 5, 1069-1120 (2019). Reviewer: José-Alejandro Lara-Rodrí guez (Mérida) MSC: 11G05 11G10 11G40 PDF BibTeX XML Cite \textit{D. Ulmer}, Algebra Number Theory 13, No. 5, 1069--1120 (2019; Zbl 1482.11083) Full Text: DOI arXiv OpenURL
Keller, Timo On an analogue of the conjecture of Birch and Swinnerton-Dyer for abelian schemes over higher dimensional bases over finite fields. (English) Zbl 1443.11126 Doc. Math. 24, 915-993 (2019). Reviewer: Remke Kloosterman (Padova) MSC: 11G40 11G50 19F27 11G10 14F20 14K15 PDF BibTeX XML Cite \textit{T. Keller}, Doc. Math. 24, 915--993 (2019; Zbl 1443.11126) Full Text: DOI arXiv Backlinks: MO MO OpenURL
Aikawa, Yusuke The bounds of the Mordell-Weil ranks in cyclotomic towers of function fields. (English) Zbl 1470.11146 J. Number Theory 202, 332-346 (2019). MSC: 11G05 14H05 14H52 33C05 PDF BibTeX XML Cite \textit{Y. Aikawa}, J. Number Theory 202, 332--346 (2019; Zbl 1470.11146) Full Text: DOI OpenURL
Salami, Sajad The rational points on certain abelian varieties over function fields. (English) Zbl 1481.14045 J. Number Theory 195, 330-337 (2019); corrigendum ibid. 227, 306-307 (2021). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 14G10 14H40 PDF BibTeX XML Cite \textit{S. Salami}, J. Number Theory 195, 330--337 (2019; Zbl 1481.14045) Full Text: DOI arXiv OpenURL
Griffon, Richard Explicit \(L\)-functions and a Brauer-Siegel theorem for Hessian elliptic curves. (English. French summary) Zbl 1441.11143 J. Théor. Nombres Bordx. 30, No. 3, 1059-1084 (2018). MSC: 11G05 11G40 14G10 11F67 11M38 PDF BibTeX XML Cite \textit{R. Griffon}, J. Théor. Nombres Bordx. 30, No. 3, 1059--1084 (2018; Zbl 1441.11143) Full Text: DOI arXiv OpenURL
Griffon, Richard Analogue of the Brauer-Siegel theorem for Legendre elliptic curves. (English) Zbl 1440.11093 J. Number Theory 193, 189-212 (2018). MSC: 11G05 11G40 11F67 14G10 11M99 11R47 PDF BibTeX XML Cite \textit{R. Griffon}, J. Number Theory 193, 189--212 (2018; Zbl 1440.11093) Full Text: DOI arXiv OpenURL
Daniels, Harris B.; Goodwillie, Hannah On the ranks of elliptic curves with isogenies. (English) Zbl 1428.11107 Int. J. Number Theory 13, No. 9, 2215-2227 (2017). MSC: 11G05 14H52 PDF BibTeX XML Cite \textit{H. B. Daniels} and \textit{H. Goodwillie}, Int. J. Number Theory 13, No. 9, 2215--2227 (2017; Zbl 1428.11107) Full Text: DOI arXiv OpenURL
Ono, Ken; Trebat-Leder, Sarah The 1729 \(K3\) surface. (English) Zbl 1352.14014 Res. Number Theory 2, Paper No. 26, 6 p. (2016); erratum ibid. 3, Paper No. 12, 1 p. (2017). Reviewer: Noriko Yui (Kingston) MSC: 14G05 14H52 PDF BibTeX XML Cite \textit{K. Ono} and \textit{S. Trebat-Leder}, Res. Number Theory 2, Paper No. 26, 6 p. (2016; Zbl 1352.14014) Full Text: DOI arXiv OpenURL
Davis, Christopher; Occhipinti, Tommy Explicit points on \(y^2+xy-t^dy=x^3\) and related character sums. (English) Zbl 1396.11091 J. Number Theory 168, 13-38 (2016). MSC: 11G20 11T06 11T23 PDF BibTeX XML Cite \textit{C. Davis} and \textit{T. Occhipinti}, J. Number Theory 168, 13--38 (2016; Zbl 1396.11091) Full Text: DOI arXiv OpenURL
Ulmer, Douglas Curves and Jacobians over function fields. (English) Zbl 1384.11077 Bars, Francesc (ed.) et al., Arithmetic geometry over global function fields. Selected notes based on the presentations at five advanced courses on arithmetic geometry at the Centre de Recerca Matemàtica, CRM, Barcelona, Spain, February 22 – March 5 and April 6–16, 2010. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0852-1/pbk; 978-3-0348-0853-8/ebook). Advanced Courses in Mathematics – CRM Barcelona, 281-337 (2014). MSC: 11G35 11G50 11G40 14H40 PDF BibTeX XML Cite \textit{D. Ulmer}, in: Arithmetic geometry over global function fields. Selected notes based on the presentations at five advanced courses on arithmetic geometry at the Centre de Recerca Matemàtica, CRM, Barcelona, Spain, February 22 -- March 5 and April 6--16, 2010. Basel: Birkhäuser/Springer. 281--337 (2014; Zbl 1384.11077) Full Text: DOI OpenURL
Moehlmann, G. Computation of Mordell-Weil bases for ordinary elliptic curves in characteristic two. (English) Zbl 1296.11065 LMS J. Comput. Math. 17A, Spec. Iss., 1-13 (2014). MSC: 11G05 11G07 14G25 14G17 PDF BibTeX XML Cite \textit{G. Moehlmann}, LMS J. Comput. Math. 17A, 1--13 (2014; Zbl 1296.11065) Full Text: DOI OpenURL
Pál, Ambrus Hodge theory and the Mordell-Weil rank of elliptic curves over extensions of function fields. (English) Zbl 1285.14040 J. Number Theory 137, 166-178 (2014). Reviewer: Remke Kloosterman (Berlin) MSC: 14J27 11G40 PDF BibTeX XML Cite \textit{A. Pál}, J. Number Theory 137, 166--178 (2014; Zbl 1285.14040) Full Text: DOI arXiv OpenURL
Bombieri, E. The classical theory of zeta and \(L\)-functions. (English) Zbl 1275.11117 Milan J. Math. 78, No. 1, 11-59 (2010). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11M06 11-03 11M36 11M38 11M50 PDF BibTeX XML Cite \textit{E. Bombieri}, Milan J. Math. 78, No. 1, 11--59 (2010; Zbl 1275.11117) Full Text: DOI OpenURL
Bandini, Andrea; Longhi, Ignazio Selmer groups for elliptic curves in \(\mathbb Z_l^d \)-extensions of function fields of characteristic \(p\). (English. French summary) Zbl 1207.11061 Ann. Inst. Fourier 59, No. 6, 2301-2327 (2009). Reviewer: Filippo Nuccio (Heidelberg) MSC: 11G05 11R23 PDF BibTeX XML Cite \textit{A. Bandini} and \textit{I. Longhi}, Ann. Inst. Fourier 59, No. 6, 2301--2327 (2009; Zbl 1207.11061) Full Text: DOI arXiv EuDML OpenURL
Berger, Lisa Towers of surfaces dominated by products of curves and elliptic curves of large rank over function fields. (English) Zbl 1204.11098 J. Number Theory 128, No. 12, 3013-3030 (2008). MSC: 11G40 11G05 11R58 PDF BibTeX XML Cite \textit{L. Berger}, J. Number Theory 128, No. 12, 3013--3030 (2008; Zbl 1204.11098) Full Text: DOI OpenURL
Farmer, David W.; Gonek, S. M.; Hughes, C. P. The maximum size of \(L\)-functions. (English) Zbl 1234.11109 J. Reine Angew. Math. 609, 215-236 (2007). Reviewer: Daniel Fiorilli (Princeton) MSC: 11M06 11M50 11M26 PDF BibTeX XML Cite \textit{D. W. Farmer} et al., J. Reine Angew. Math. 609, 215--236 (2007; Zbl 1234.11109) Full Text: DOI arXiv OpenURL
Ulmer, Douglas \(L\)-functions with large analytic rank and abelian varieties with large algebraic rank over function fields. (English) Zbl 1110.11019 Invent. Math. 167, No. 2, 379-408 (2007). Reviewer: Noriko Yui (Kingston) MSC: 11G40 14G05 11G05 11G10 11G30 14G10 14G25 14K12 14K15 PDF BibTeX XML Cite \textit{D. Ulmer}, Invent. Math. 167, No. 2, 379--408 (2007; Zbl 1110.11019) Full Text: DOI arXiv OpenURL
Moree, Pieter; Solé, Patrick Around Pelikán’s conjecture on very odd sequences. (English) Zbl 1072.11071 Manuscr. Math. 117, No. 2, 219-238 (2005). Reviewer: Jürgen Spilker (Freiburg i. Br.) MSC: 11N64 94B15 11N37 PDF BibTeX XML Cite \textit{P. Moree} and \textit{P. Solé}, Manuscr. Math. 117, No. 2, 219--238 (2005; Zbl 1072.11071) Full Text: DOI arXiv OpenURL
Lee, Jung-Jo; Murty, M. Ram An application of Mumford’s gap principle. (English) Zbl 1048.11050 J. Number Theory 105, No. 2, 333-343 (2004). Reviewer: Robert F. Lax (Baton Rouge) MSC: 11G30 11G05 11G50 14G05 PDF BibTeX XML Cite \textit{J.-J. Lee} and \textit{M. R. Murty}, J. Number Theory 105, No. 2, 333--343 (2004; Zbl 1048.11050) Full Text: DOI OpenURL
Matsuno, Kazuo A note on the growth of Mordell-Weil ranks of elliptic curves in cyclotomic \(\mathbb Z_p\)-extensions. (English) Zbl 1186.11031 Proc. Japan Acad., Ser. A 79, No. 5, 101-104 (2003). MSC: 11G05 11R23 PDF BibTeX XML Cite \textit{K. Matsuno}, Proc. Japan Acad., Ser. A 79, No. 5, 101--104 (2003; Zbl 1186.11031) Full Text: DOI Euclid OpenURL