Geodesic
CONGRUENCE PRIMES FOR SIEGEL MODULAR FORMS OF PARAMODULAR LEVEL AND APPLICATIONS TO THE BLOCH–KATO CONJECTURE
Glasgow mathematical journal, Tome 63 (2021) no. 3, pp. 660-681

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DOI

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. 
BROWN, JIM; LI, HUIXI. CONGRUENCE PRIMES FOR SIEGEL MODULAR FORMS OF PARAMODULAR LEVEL AND APPLICATIONS TO THE BLOCH–KATO CONJECTURE. Glasgow mathematical journal, Tome 63 (2021) no. 3, pp. 660-681. doi: 10.1017/S0017089520000439
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     author = {BROWN, JIM and LI, HUIXI},
     title = {CONGRUENCE {PRIMES} {FOR} {SIEGEL} {MODULAR} {FORMS} {OF} {PARAMODULAR} {LEVEL} {AND} {APPLICATIONS} {TO} {THE} {BLOCH{\textendash}KATO} {CONJECTURE}},
     journal = {Glasgow mathematical journal},
     pages = {660--681},
     year = {2021},
     volume = {63},
     number = {3},
     doi = {10.1017/S0017089520000439},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000439/}
}
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