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Experimental Mathematics Volume 10, 2001 - Issue 2
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Original Articles

Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q

Christophe Delaunay Universit'e Bordeaux I, Laboratoire A2X, 351 Cours de la Lib'eration, 33 405, Talence, France E-mail: [email protected]
Pages 191-196 | Published online: 04 Apr 2012

Citations (24)

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C. Delaunay & S. Duquesne. (2003) Numerical Investigations Related to the Derivatives of the L-Series of Certain Elliptic Curves. Experimental Mathematics 12:3, pages 311-317.
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Articles from other publishers (23)

Anwesh Ray. (2023) Arithmetic statistics and diophantine stability for elliptic curves. The Ramanujan Journal 62:1, pages 215-239.
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Jungin Lee. (2023) Joint distribution of the cokernels of random p -adic matrices . Forum Mathematicum 35:4, pages 1005-1020.
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Mark Watkins. (2022) Distribution of the 2-Selmer rank under twisting. Publications mathématiques de Besançon. Algèbre et théorie des nombres, pages 59-133.
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Joachim Petit. (2022) On the Number of Quadratic Twists with a Rational Point of Almost Minimal Height. International Mathematics Research Notices 2022:9, pages 7056-7099.
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Ari Shnidman & Ariel Weiss. (2022) Elements of prime order in Tate–Shafarevich groups of abelian varieties over. Forum of Mathematics, Sigma 10.
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Ashay Burungale & Ye Tian. (2022) The even parity Goldfeld conjecture: Congruent number elliptic curves. Journal of Number Theory 230, pages 161-195.
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Claudio Gómez-Gonzáles & Jesse Wolfson. (2021) Problems in arithmetic topology. Research in the Mathematical Sciences 8:2.
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Álvaro Lozano-Robledo. (2021) A probabilistic model for the distribution of ranks of elliptic curves over . Journal of Number Theory 221, pages 270-338.
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Bruce Jordan, Zev Klagsbrun, Bjorn Poonen, Christopher Skinner & Yevgeny Zaytman. (2020) Statistics of K-groups modulo p for the ring of integers of a varying quadratic number field. Tunisian Journal of Mathematics 2:2, pages 287-307.
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Pierre Le Boudec. (2019) A statistical view on the conjecture of Lang about the canonical height on elliptic curves. Transactions of the American Mathematical Society 372:12, pages 8347-8361.
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Chao Li. (2019) Level Raising mod 2 and Obstruction to Rank Lowering. International Mathematics Research Notices 2019:8, pages 2332-2355.
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Melanie Wood. (2016) The distribution of sandpile groups of random graphs. Journal of the American Mathematical Society 30:4, pages 915-958.
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Jason Fulman. (2015) Hall-Littlewood Polynomials and Cohen-Lenstra Heuristics for Jacobians of Random Graphs. Annals of Combinatorics 20:1, pages 115-124.
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Pierre Le Boudec. (2016) Height of rational points on quadratic twists of a given elliptic curve. Bulletin of the London Mathematical Society 48:1, pages 99-108.
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Jennifer S. Balakrishnan, Wei Ho, Nathan Kaplan, Simon Spicer, William Stein & James Weigandt. (2016) Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks. LMS Journal of Computation and Mathematics 19:A, pages 351-370.
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Dustin Hinkel & Matthew P. Young. (2015) The distribution of central values of elliptic curve L-functions. Journal of Number Theory 156, pages 15-20.
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Julien Clancy, Nathan Kaplan, Timothy Leake, Sam Payne & Melanie Matchett Wood. (2015) On a Cohen–Lenstra heuristic for Jacobians of random graphs. Journal of Algebraic Combinatorics 42:3, pages 701-723.
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Christophe Delaunay & Frédéric Jouhet. (2014) -torsion points in finite abelian groups and combinatorial identities . Advances in Mathematics 258, pages 13-45.
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Keqin Feng & Maosheng Xiong. (2012) ON SELMER GROUPS AND TATE–SHAFAREVICH GROUPS FOR ELLIPTIC CURVES y 2 = x 3 − n 3 . Mathematika 58:2, pages 236-274.
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Bjorn Poonen & Eric Rains. (2011) Random maximal isotropic subspaces and Selmer groups. Journal of the American Mathematical Society 25:1, pages 245-269.
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Christophe Delaunay. (2011) Averages of groups involving -rank and combinatorial identities . Journal of Number Theory 131:3, pages 536-551.
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Maosheng Xiong & Alexandru Zaharescu. (2008) Distribution of Selmer groups of quadratic twists of a family of elliptic curves. Advances in Mathematics 219:2, pages 523-553.
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CHRISTOPHE DELAUNAY. (2012) MOMENTS OF THE ORDERS OF TATE–SHAFAREVICH GROUPS. International Journal of Number Theory 01:02, pages 243-264.
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