The doubling Archimedean zeta integrals for \(p\)-adic interpolation

DOI10.4310/MRL.2021.V28.N1.A7zbMATH Open1469.11460arXiv1904.07121OpenAlexW3154046011WikidataQ114020795 ScholiaQ114020795MaRDI QIDQ2043294

Zheng Liu

Publication date: 30 July 2021

Published in: Mathematical Research Letters (Search for Journal in Brave)

Abstract: We compute the Archimedean doubling zeta integrals which appear in the interpolation formulas for the p-adic L-functions of Siegel modular forms, and verify that they agree with the modified Archimedean Euler factors for p-adic interpolation conjectured by Coates--Perrin-Riou.

Full work available at URL: https://arxiv.org/abs/1904.07121

zbMATH Keywords

Siegel modular forms\(p\)-adic \(L\)-functions

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) (p)-adic theory, local fields (11F85)

Related Items (6)

The special values of the standard 𝐿-functions for 𝐺𝑆𝑝_{2𝑛}×𝐺𝐿₁ ⋮ On Deligne's conjecture for symmetric fifth \(L\)-functions of modular forms ⋮ On algebraicity of special values of symmetric 4-th and 6-th power \(L\)-functions for \(\operatorname{GL}(2)\) ⋮ On Deligne's conjecture for symmetric fourth \(L\)-functions of Hilbert modular forms ⋮ Archimedean zeta integrals for unitary groups ⋮ Test vectors for non‐Archimedean Godement–Jacquet zeta integrals

This page was built for publication: The doubling Archimedean zeta integrals for \(p\)-adic interpolation

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2043294)