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Hecke Gr├Â├čencharakters and the L-Function Ratios Conjecture

Date: Thursday, May 2, 2019 11:00 - 12:00
Speaker: Ezra Waxman (Charles University in Prague)
Location: Raiffeisen Lecture Hall, Central Building
Series: Mathematics and CS Seminar
Host: Tim Browning
Contact: MARR Lena
Central building lecture hall

Abstract:

A Gaussian prime is a prime element in the ring of Gaussian integers Z[i]. As the Gaussian integers lie on the plane, interesting questions about their geometric properties can be asked which have no classical analogue among the ordinary primes. Hecke proved that the Gaussian primes are equidistributed across sectors of the complex plane by making use of Hecke Größencharakters characters and their associated L-functions. In this talk I will present several applications obtained upon applying the L-functions Ratios Conjecture to this family of L-functions. In particular, I will present a conjecture for the variance of Gaussian primes across sectors, and a conjecture for the one level density across this family. Time permitting, I will also discuss results related to super even characters, which are the the function field analogue to Hecke characters.

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