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L -functions of automorphic forms and combinatorics: Dyck paths

Laurent Habsieger, Emmanuel Royer (2004)

Annales de l'Institut Fourier

We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the L -functions of modular forms of G L ( 2 ) and G L ( 3 ) . We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.

Logarithmic density of a sequence of integers and density of its ratio set

Ladislav Mišík, János T. Tóth (2003)

Journal de théorie des nombres de Bordeaux

In the paper sufficient conditions for the ( R ) -density of a set of positive integers in terms of logarithmic densities are given. They differ substantially from those derived previously in terms of asymptotic densities.

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