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

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

Published:2020-09-29 Issue:3 Volume:63 Page:660-681
ISSN:0017-0895
Container-title:Glasgow Mathematical Journal
language:en
Short-container-title:Glasgow Math. J.

Author:

BROWN JIM,LI HUIXI

Abstract

AbstractIt 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference33 articles.

1. Hilbert modular forms and the Gross-Stark conjecture

2. Paramodular abelian varieties of odd conductor

3. On the Bloch–Kato conjecture for elliptic modular forms of square-free level

4. On classical Saito-Kurokawa liftings;Schmidt;J. Reine Angew. Math.,2007

5. Nearly holomorphic functions on hermitian symmetric spaces

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