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

Published online by Cambridge University Press:  29 September 2020

JIM BROWN
Affiliation:
Department of Mathematics, Occidental College, Los Angeles, CA90041, USA, e-mail: [email protected]
HUIXI LI
Affiliation:
Department of Mathematics and Statistics, University of Nevada - Reno, Reno, NV89557, USA, e-mail: [email protected]

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.

Type
Research Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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