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2022 Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series
Ameya Pitale, Abhishek Saha, Ralf Schmidt
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Publ. Mat. 66(1): 405-434 (2022). DOI: 10.5565/PUBLMAT6612216

Abstract

We study nearly holomorphic Siegel Eisenstein series of general levels and characters on 2n, the Siegel upper half space of degree 2n. We prove that the Fourier coefficients of these Eisenstein series (once suitably normalized) lie in the ring of integers of p for all sufficiently large primes p. We also prove that the pullbacks of these Eisenstein series to n×n are cuspidal under certain assumptions.

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Ameya Pitale. Abhishek Saha. Ralf Schmidt. "Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series." Publ. Mat. 66 (1) 405 - 434, 2022. https://doi.org/10.5565/PUBLMAT6612216

Information

Received: 17 June 2020; Accepted: 2 March 2021; Published: 2022
First available in Project Euclid: 4 January 2022

Digital Object Identifier: 10.5565/PUBLMAT6612216

Subjects:
Primary: 11F46
Secondary: 11F37 , 11F70

Keywords: nearly holomorphic , pullback formula , Siegel Eisenstein series , Siegel modular forms

Rights: Copyright © 2022 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.66 • No. 1 • 2022
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