-ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

DOI10.1017/S1474748018000415zbMath1469.11091WikidataQ128576054 ScholiaQ128576054MaRDI QIDQ3295460

Zheng Liu

Publication date: 10 July 2020

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

zbMATH Keywords

\(p\)-adic \(L\)-functionsdoubling methodordinary families of Siegel modular forms

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) Fourier coefficients of automorphic forms (11F30) Arithmetic aspects of modular and Shimura varieties (11G18) Hecke-Petersson operators, differential operators (several variables) (11F60)

Related Items

The special values of the standard 𝐿-functions for 𝐺𝑆𝑝_{2𝑛}×𝐺𝐿₁ ⋮ Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of \(p\)-adic \(L\)-functions ⋮ SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS ⋮ Higher Hida theory and \(p\)-adic \(L\)-functions for \(\mathrm{GSp}_4\) ⋮ An introduction to Eisenstein measures ⋮ Ordinary families of Klingen Eisenstein series on symplectic groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classicity of overconvergent modular forms
• A \(p\)-adic Eisenstein measure for vector-weight automorphic forms
• Differential operators, pullbacks, and families of automorphic forms on unitary groups
• Analytic continuation on Siegel varieties
• Theta lifting for unitary representations with nonzero cohomology
• On differential operators attached to certain representations of classical groups
• Families of nearly ordinary Eisenstein series on unitary groups. With an appendix by Kai-Wen Lan
• Degenerate principal series and invariant distributions
• Howe correspondences on a \(p\)-adic field
• Restrictions and expansions of holomorphic representations
• On some semi-spherical representations of an Hermitian symmetric pair of the tubular type. II: Construction of the unitary representations
• Confluent hypergeometric functions on tube domains
• On the arithmetic of Siegel-Hilbert cusp forms: Petersson inner products and Fourier coefficients
• On the Segal-Shale-Weil representations and harmonic polynomials
• Non-Archimedean \(L\)-functions and arithmetical Siegel modular forms
• \(p\)-adic measures attached to Siegel modular forms
• Eisenstein series and zeta functions on symplectic groups
• Toroidal compactifications of PEL-type Kuga families
• A \(p\)-adic Eisenstein measure for unitary groups
• \(p\)-adic families of Siegel modular cuspforms
• \(p\)-adic \(L\)-functions for unitary Shimura varieties. I: Construction of the Eisenstein measure
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Modularité, formes de Siegel et surfaces abéliennes
• -ADIC EISENSTEIN SERIES AND -FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS
• A Simple Proof of Rationality of Siegel-Weil Eisenstein Series
• Special values of zeta functions attached to Siegel modular forms
• CONTROL THEOREMS OF COHERENT SHEAVES ON SHIMURA VARIETIES OF PEL TYPE
• Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
• On the infinite fern of Galois representations of unitary type
• Nearly ordinary rank four Galois representations and $p$-adic Siegel modular forms