Nonvanishing of \(L\)-series and the combinatorial sieve. With an appendix by David E. Rohrlich: Unboundedness of the Tate-Shafarevich group in families of quadratic twists

DOI10.4310/MRL.1997.v4.n3.a12zbMath0893.11034MaRDI QIDQ1364811

Jeffrey Hoffstein, Wenzhi Luo

Publication date: 8 December 1997

Published in: Mathematical Research Letters (Search for Journal in Brave)

zbMATH Keywords

Tate-Shafarevich groupquadratic twistsmetaplectic automorphic formcombinatorial sievemodular elliptic curvecentral value of modular \(L\)-series

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (9)

Dirichlet \(L\)-functions of quadratic characters of prime conductor at the central point ⋮ On ranks of quadratic twists of a Mordell curve ⋮ Non-trivial zeroes for quadratic twists of Hasse-Weil \(L\)-functions ⋮ Extreme central \(L\)-values of almost prime quadratic twists of elliptic curves ⋮ Elements of class groups and Shafarevich-Tate groups of elliptic curves ⋮ On the proportion of rank 0 twists of elliptic curves ⋮ Large Shafarevich-Tate groups over quadratic number fields ⋮ ON SIGN CHANGES FOR ALMOST PRIME COEFFICIENTS OF HALF‐INTEGRAL WEIGHT MODULAR FORMS ⋮ ON POSITIVE PROPORTION OF RANK-ZERO TWISTS OF ELLIPTIC CURVES OVER

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