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Izvestiya: Mathematics, 2016, Volume 80, Issue 3, Pages 602–622
DOI: https://doi.org/10.1070/IM8463 (Mi im8463) 		 
This article is cited in 4 scientific papers (total in 4 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
English version PDF (342 kB) Citations (4)
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DOI: https://doi.org/10.1070/IM8463
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.
Received: 22.10.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2016, Volume 80, Issue 3, Pages 151–172
DOI: https://doi.org/10.4213/im8463
Bibliographic databases:
Document Type: Article
UDC: 511
MSC: 11M41, 11M26
Language: English
Original paper language: Russian
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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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:255
    English version PDF:21
    References:53
    First page:35
     
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