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Li coefficients for automorphic L -functions

Jeffrey C. Lagarias (2007)

Annales de l’institut Fourier

Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients λ n ( n = 1 , 2 , ...

Linear periods.

Hervé Jacquet, Solomon Friedberg (1993)

Journal für die reine und angewandte Mathematik

Local Borcherds products

Jan Hendrik Bruinier, Eberhard Freitag (2001)

Annales de l’institut Fourier

The local Picard group at a generic point of the one-dimensional Baily-Borel boundary of a Hermitean symmetric quotient of type O ( 2 , n ) is computed. The main ingredient is a local version of Borcherds’ automorphic products. The local obstructions for a Heegner divisor to be principal are given by certain theta series with harmonic coefficients. Sometimes they generate Borcherds’ space of global obstructions. In these particular cases we obtain a simple proof of a result due to the first author: Suppose...

Local Indecomposability of Hilbert Modular Galois Representations

Bin Zhao (2014)

Annales de l’institut Fourier

We prove the indecomposability of the Galois representation restricted to the p -decomposition group attached to a non CM nearly p -ordinary weight two Hilbert modular form over a totally real field F under the assumption that either the degree of F over is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of F .

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