Adjoint L-Values and Primes of Congruence for Hilbert Modular Forms |
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Authors: | Eknath Ghate |
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Affiliation: | (1) Tata Institute of Fundamental Research, School of Mathematics, Homi Bhabha Road, 400 005 Mumbai, India |
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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 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 , 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 , where is a totally positive unit of F. |
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Keywords: | adjoint L-values congruence primes Hilbert modular forms |
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