NUMERICAL EXAMPLES OF SIEGEL CUSP FORMS OF DEGREEE 3 AND THEIR ZETA-FUNCTIONS

DOI10.2206/kyushumfs.46.307zbMath0780.11022OpenAlexW2105600355MaRDI QIDQ4039157

Isao Miyawaki

Publication date: 7 February 1994

Published in: Memoirs of the Faculty of Science, Kyusyu University. Series A, Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2206/kyushumfs.46.307

zbMATH Keywords

\(L\)-functionFourier coefficientsHecke operatorsMaass spacelocal factorsSiegel cusp formformal Dirichlet series

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Related Items (23)

Arithmetical modular forms and new constructions of \(p\)-adic \(L\)-functions on classical groups ⋮ Miyawaki's \(F_{12}\) spinor \(L\)-function conjecture ⋮ Congruences for Hecke eigenvalues of Siegel modular forms ⋮ Harder's conjecture. I ⋮ Using Katsurada’s determination of the Eisenstein series to compute Siegel eigenforms ⋮ On \(p\)-divisibility of Fourier coefficients of Siegel modular forms ⋮ 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 ⋮ Explicit Hecke series for symplectic group of genus 4 ⋮ Two modularity lifting conjectures for families of Siegel modular forms ⋮ Automorphic forms for some even unimodular lattices ⋮ Notes on theta series for Niemeier lattices ⋮ Families of Siegel modular forms, \(L\)-functions and modularity lifting conjectures ⋮ On zeta functions and families of Siegel modular forms ⋮ Construction of Theta Series of Any Vector-Valued Weight and Applications to Lifts and Congruences ⋮ On the modularity of the \(\text{GL}_2\)-twisted spinor \(L\)-function ⋮ Siegel Modular Forms and Their Applications ⋮ Non-vanishing of Miyawaki type lifts ⋮ On special values of standard \(L\)-functions of Siegel cusp eigenforms of genus 3 ⋮ Eisenstein congruences for split reductive groups ⋮ A theory of Miyawaki liftings: the Hilbert-Siegel case ⋮ Book Review: The 1-2-3 of modular forms ⋮ Pullback of the lifting of elliptic cusp forms and Miyawaki's conjecture

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