Adjoint L-values and primes of congruence for Hilbert modular forms

Ghate, Eknath (2002) Adjoint L-values and primes of congruence for Hilbert modular forms Compositio Mathematica, 132 (3). pp. 243-281. ISSN 0010-437X

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Official URL: https://www.cambridge.org/core/journals/compositio...

Related URL: http://dx.doi.org/10.1023/A:1016562918902

Abstract

Let f be a primitive Hilbert modular cusp form of arbitrary level and parallel weight k, defined over a totally real number field F. We define a finite set of primes S that depends on the weight and level of f, the field F, and the torsion in the boundary cohomology groups of the Borel–Serre compactification of the underlying Hilbert-Blumenthal variety. We show that, outside S, any prime that divides the algebraic part of the value at s=1 of the adjoint L-function of f is a congruence prime for f. In special cases we identify the ‘boundary primes’ in terms of expressions of the form NF/Qk−1−1), where ε is a totally positive unit of F.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
Keywords:Adjoint; L-Values; Congruence Primes; Hilbert Modular Forms
ID Code:101414
Deposited On:09 Mar 2018 10:34
Last Modified:09 Mar 2018 10:34

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