SYMMETRIC SQUARE L-FUNCTIONS AND SHAFAREVICH–TATE GROUPS, II

DOI10.1142/S1793042109002699zbMath1229.11078MaRDI QIDQ3652601

Neil Dummigan

Publication date: 15 December 2009

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

zbMATH Keywords

Bloch-Kato conjecturesymmetric square \(L\)-functionSelmer groupKlingen-Eisenstein series

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Congruences for modular and (p)-adic modular forms (11F33) 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

Some generalizations of the Weil representations of the symplectic and unitary groups, Lifting congruences to half-integral weight, Yoshida lifts and Selmer groups, \(\mathrm{GL}_2\times \mathrm{GSp}_2\) \(L\)-values and Hecke eigenvalue congruences, Siegel modular forms of degree three and the cohomology of local systems, Twisted adjoint \(L\)-values, dihedral congruence primes and the Bloch-Kato conjecture, Eisenstein congruences for split reductive groups, Computations of vector-valued Siegel modular forms, Kurokawa-Mizumoto congruences and degree-8 \(L\)-values, Congruences of local origin and automorphic induction

Cites Work

• Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen. II
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• An explicit dimension formula for the spaces of generalized automorphic forms with respect to \(\mathrm{Sp}(2, \mathbb Z)\)
• Vector valued Siegel's modular forms of degree two and the associated Andrianov \(L\)-functions
• On certain vector valued Siegel modular forms of degree two
• Congruences for eigenvalues of Hecke operators on Siegel modular forms of degree two
• Congruences between Siegel modular forms of degree two
• Congruences of cusp forms and special values of their zeta functions
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
• On the \(l\)-adic cohomology of Siegel threefolds
• On the cohomology of local systems on the moduli spaces of curves of genus 2 and of abelian surfaces. I
• On the cohomology of local systems on the moduli spaces of curves of genus 2 and of Abelian surfaces. II.
• On special values of standard \(L\)-functions attached to vector valued Siegel modular forms.
• Selmer groups and the Eisenstein-Klingen ideal.
• Congruence of Siegel modular forms and special values of their standard zeta functions
• Zum Darstellungssatz für Siegelsche Modulformen
• Symmetric Square L-Functions and Shafarevich-Tate Groups
• Siegel Modular Forms and Their Applications
• Congruence Between a Siegel and an Elliptic Modular Form
• SUR LES DÉFORMATIONS p-ADIQUES DE CERTAINES REPRÉSENTATIONS AUTOMORPHES
• Saito–Kurokawa lifts and applications to the Bloch–Kato conjecture
• Construction de représentations $p$-adiques
• RANKIN–COHEN TYPE DIFFERENTIAL OPERATORS FOR SIEGEL MODULAR FORMS
• Siegel modular forms and representations
• The Bloch-Kato conjecture for adjoint motives of modular forms