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Zeta-functions of harmonic theta-series and prime numbers

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Speaker: 
Anatoli Andrianov
Affiliation: 
Steklov Math. Inst./MPI
Date: 
Wed, 2010-06-16 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

The problem of separation of prime numbers presentable as values of quadratic polynomials, for example, of primes having the form $n^2+1$, naturally leads to the  question on Euler product factorization of zeta-functions corresponding to theta-series with harmonic coefficients. Two approaches to this question will be touched in the talk: one is based on the action of Hecke operators on harmonic theta-series and another is linked with interpretation of the zeta-functions, at least for certain binary quadratic forms, as L-functions of suitable quadratic rings with Hecke "Grossen" characters.

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