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А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications
May 27, 2017 12:45–13:15, Moscow, Department of Mechanics and Mathematics, Lomonosov Moscow State University
 


Zeros of the Epstein zeta-function

I. S. Rezvyakova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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I. S. Rezvyakova


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Abstract: I shall talk about the proof of the following result: the critical line contains a positive proportion of non-trivial zeros of the Epstein zeta-function, corresponding to a binary positive definite quadratic form. The proof of this result for the function which violates the Riemann hypothesis (it has many non-trivial zeros off the critical line) relies heavily on the methods developed by Atle Selberg. We shall discuss some results, which can be obtained in the theory of L-functions following Selberg's ideas.

Language: English

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