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CONGRUENCE PRIMES FOR SIEGEL MODULAR FORMS OF PARAMODULAR LEVEL AND APPLICATIONS TO THE BLOCH–KATO CONJECTURE

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  29 September 2020

JIM BROWN  and
HUIXI LI
JIM BROWN
Affiliation:
Department of Mathematics, Occidental College, Los Angeles, CA90041, USA, e-mail: jimlb@oxy.edu
HUIXI LI
Affiliation:
Department of Mathematics and Statistics, University of Nevada - Reno, Reno, NV89557, USA, e-mail: huixil@unr.edu
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Abstract

It has been well established that congruences between automorphic forms have far-reaching applications in arithmetic. In this paper, we construct congruences for Siegel–Hilbert modular forms defined over a totally real field of class number 1. As an application of this general congruence, we produce congruences between paramodular Saito–Kurokawa lifts and non-lifted Siegel modular forms. These congruences are used to produce evidence for the Bloch–Kato conjecture for elliptic newforms of square-free level and odd functional equation.

MSC classification

Primary: 11F33: Congruences for modular and $p$-adic modular forms
Secondary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F32: Modular correspondences, etc.
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 3 , September 2021 , pp. 660 - 681
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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