This article is cited in 5 papers

On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach

I. S. Rezvyakova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We consider in detail Selberg's method for proving that under certain natural assumptions, a positive proportion of the non-trivial zeros of a linear combination of L-functions from the Selberg class lie on the critical line. As an example, we provide all the ingredients necessary to prove this result in the case of a linear combination of L-functions of degree two attached to automorphic forms.

Keywords: Riemann hypothesis, zeros on the critical line, Selberg class, density theorems, Hecke L-functions.

UDC: 511

MSC: 11M41, 11M26

Received: 22.10.2015

DOI: 10.4213/im8463

 English version: Izvestiya: Mathematics, 2016, 80:3, 602–622

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