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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 3, Pages 151–172 (Mi izv8463)  

This article is cited in 2 scientific papers (total in 2 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/im8463

Full text: PDF file (589 kB)
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English version:
Izvestiya: Mathematics, 2016, 80:3, 602–622

Bibliographic databases:

UDC: 511
MSC: 11M41, 11M26
Received: 22.10.2015

Citation: I. S. Rezvyakova, “On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach”, Izv. RAN. Ser. Mat., 80:3 (2016), 151–172; Izv. Math., 80:3 (2016), 602–622

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. S. A. Gritsenko, “On the zeros of the Davenport–Heilbronn function”, Proc. Steklov Inst. Math., 296 (2017), 65–87  mathnet  crossref  crossref  mathscinet  isi  elib
    2. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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