A nonvanishing theorem for derivatives of automorphic 𝐿-functions with applications to elliptic curves

DOI10.1090/S0273-0979-1989-15771-6zbMath0699.10038MaRDI QIDQ3476888

Solomon Friedberg, Jeffrey Hoffstein, Daniel Bump

Publication date: 1989

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

rational pointselliptic curvenonvanishing theoremsautomorphic L-functiontwisted L-functioncuspidal new-formderivative of L-functions

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11)

Related Items

Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces ⋮ Nonvanishing theorems for L-functions of modular forms and their derivatives ⋮ Weyl group multiple Dirichlet series constructed from quadratic characters ⋮ On some applications of automorphic forms to number theory ⋮ \(p\)-adic Whittaker functions on the metaplectic group ⋮ K-RATIONAL D-BRANE CRYSTALS ⋮ Cubic twists of \(\text{GL}(2)\) automorphic \(L\)-functions ⋮ The \(GL(3)\) Mellin transform for twisted non-cuspidal forms of higher level ⋮ The first moment of quadratic twists of modular $L$-functions

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