Some Siegel modular standard \(L\)-values, and Shafarevich-Tate groups

DOI10.1016/j.jnt.2011.01.012zbMath1254.11046OpenAlexW2168304178MaRDI QIDQ533820

Tomoyoshi Ibukiyama, Neil Dummigan, Hidenori Katsurada

Publication date: 6 May 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.01.012

zbMATH Keywords

Bloch-Kato conjectureHarder's conjectureSaito-Kurokawa liftstandard L-function

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items

An explicit formula for the Siegel series of a quadratic form over a non-Archimedean local field, CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINORL-VALUES, Congruence primes for automorphic forms on unitary groups and applications to the arithmetic of Ikeda lifts, Yoshida lifts and Selmer groups, Harder's conjecture. I, \(\mathrm{GL}_2\times \mathrm{GSp}_2\) \(L\)-values and Hecke eigenvalue congruences, Siegel modular forms of degree three and the cohomology of local systems, Congruences to Ikeda-Miyawaki lifts and triple \(L\)-values of elliptic modular forms, Exact critical values of the symmetric fourth \(L\) function and vector valued Siegel modular forms, Generic differential operators on Siegel modular forms and special polynomials, Eisenstein congruences for split reductive groups, Congruence Primes of the Kim–Ramakrishnan–Shahidi Lift, Kurokawa-Mizumoto congruences and degree-8 \(L\)-values, One-line formula for automorphic differential operators on Siegel modular forms

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