James Maynard

University of Oxford

Kloosterman sums and Siegel zeros

Heilbronn Number Theory Seminar

24th January 2018, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room

Kloosterman sums arise naturally in the study of the
distribution of various arithmetic objects in analytic number theory.
The 'vertical' Sato-Tate law of Katz describes their distribution over a
fixed field F_p, but the equivalent 'horizontal' distribution as the
base field varies over primes remains open. We describe work showing
cancellation in the sum over primes if there are exceptional
Siegel-Landau zeros. This is joint work with Sary Drappeau, relying on a
fun blend of ideas from algebraic geometry, the spectral theory of
automorphic forms and sieve theory.

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