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January, 2020 Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level
Martin DICKSON, Ameya PITALE, Abhishek SAHA, Ralf SCHMIDT
J. Math. Soc. Japan 72(1): 251-301 (January, 2020). DOI: 10.2969/jmsj/78657865

Abstract

We formulate an explicit refinement of Böcherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of $L$-functions. To achieve this, we compute the relevant local integrals that appear in the refined global Gan–Gross–Prasad conjecture for Bessel periods as proposed by Liu. We note several consequences of our conjecture to arithmetic and analytic properties of $L$-functions and Fourier coefficients of Siegel modular forms.

Funding Statement

The third author acknowledges the support of the EPSRC grant EP/L025515/1.

Citation

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Martin DICKSON. Ameya PITALE. Abhishek SAHA. Ralf SCHMIDT. "Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level." J. Math. Soc. Japan 72 (1) 251 - 301, January, 2020. https://doi.org/10.2969/jmsj/78657865

Information

Received: 18 August 2017; Revised: 9 October 2018; Published: January, 2020
First available in Project Euclid: 28 October 2019

zbMATH: 07196505
MathSciNet: MR4055095
Digital Object Identifier: 10.2969/jmsj/78657865

Subjects:
Primary: 11F46
Secondary: 11F30, 11F67, 11F70

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 1 • January, 2020
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