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Automorphic summation formulae and moments of zeta

Monday 12th July 2004 - 17:00 to 17:30
INI Seminar Room 1
Session Title: 
Matrix Ensembles and L-Functions

The strong parallel between conjectural asymptotics of the 2n-th moment of zeta (Conrey, Farmer, Keating, Rubinstein and Snaith) with a ``constant term'' of an Eisenstein series on GL(2n) will be reviewed. For the second moment, the parallel is explained by the Voronoi-Oppenheim summation formula. For larger n, divisor functions of lattices will be defined and a pleasant new Voronoi-type summation formula will be proved for the lattice divisor functions, making use of Bessel functions associated with the Shalika-Kirillov model of a degenerate principal series representation of GL(2n,R).

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons