Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms

DOI10.1090/memo/1306OpenAlexW3164437153MaRDI QIDQ4995484

Kazuyuki Hatada

Publication date: 24 June 2021

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

Full work available at URL: https://doi.org/10.1090/memo/1306

zbMATH Keywords

Siegel cusp formsrigid analytic varieties\(p\)-parameters of Siegel cusp eigenformsaction of Hecke rings on Siegel modular varietiesestimation of eigenvalues of Hecke operatorsthe generalized Ramanujan conjecture

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Étale and other Grothendieck topologies and (co)homologies (14F20) Holomorphic modular forms of integral weight (11F11) Varieties over finite and local fields (11G25) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Rigid analytic geometry (14G22) (p)-adic cohomology, crystalline cohomology (14F30) Hecke-Petersson operators, differential operators (several variables) (11F60) Modular correspondences, etc. (11F32)

Cites Work

• On the action of Hecke rings on homology groups of smooth compactifications of Siegel modular varieties and Siegel cusp forms
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Toroidal compactification of Siegel spaces
• Siegel cusp forms as holomorphic differential forms on certain compact varieties
• Non-Archimedean L-functions of Siegel and Hilbert modular forms
• Correspondences for Hecke rings and \(\ell\)-adic cohomology groups on smooth compactifications of Siegel modular varieties
• On the \(l\)-adic cohomology of Siegel threefolds
• Some consequences of the Riemann hypothesis for varieties over finite fields
• Resolution of singularities of an algebraic variety over a field of characteristic zero. II
• Endoscopy for \(\mathrm{GSp}(4)\) and the cohomology of Siegel modular threefolds
• Algebraic number fields and symplectic discontinuous groups
• On elliptic modular surfaces
• Homologie singulière des espaces fibrés. Applications
• Formes modulaires de poids $1$
• Automorphic Forms on Adele Groups. (AM-83)
• p-Adic Hodge Theory
• Estimates for eigenvalues of Hecke operators on Siegel cusp forms.
• The role of the Ramanujan conjecture in analytic number theory
• On Rational Singuarities
• ON MODULAR CORRESPONDENCES FOR SP(N, Z ) AND THEIR CONGRUENCE RELATIONS
• On classical and \(\ell\)-adic modular forms of levels \(N\ell^m\) and \(N\)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms