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Level-modulus collusion in the Voronoi summation formula for GL(n)

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Andrew Corbett
University of Bristol/MPI
Wed, 2017-07-12 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

In the spirit of the Poisson summation formula, in 1903-05, Voronoi proved explicit formulae for certain
finite sums of arithmetic quantities; for example, addressing Dirichlet's divisor problem and Gauss' circle.
Now we understand such summation formulae to describe the (additively twisted) Fourier coefficients of
automorphic forms, most generally for GL(n). From the point of view of representation theory, we describe
the consequences of allowing the level and modulus to ramify together. We shall give classical examples
for GL(2) and applications to bounding the four-norm of a holomorphic cusp form.

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