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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 6, Pages 183–222 (Mi izv4093)  

This article is cited in 7 scientific papers (total in 7 papers)

Zeros of linear combinations of Hecke $L$-functions on the critical line

I. S. Rezvyakova

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We obtain a new lower bound for the number of zeros on intervals of the critical line for linear combinations of Hecke $L$-functions.

Keywords: Hecke $L$-functioins, zeros on the critical line, automorphic forms, Jutila's variant of circle method.

DOI: https://doi.org/10.4213/im4093

Full text: PDF file (724 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2010, 74:6, 1277–1314

Bibliographic databases:

Document Type: Article
UDC: 511
MSC: 11M26
Received: 24.02.2009
Revised: 23.05.2009

Citation: I. S. Rezvyakova, “Zeros of linear combinations of Hecke $L$-functions on the critical line”, Izv. RAN. Ser. Mat., 74:6 (2010), 183–222; Izv. Math., 74:6 (2010), 1277–1314

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  • https://doi.org/10.4213/im4093
  • http://mi.mathnet.ru/eng/izv/v74/i6/p183

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. S. Rezvyakova, “On the Zeros on the Critical Line of $L$-Functions Corresponding to Automorphic Cusp Forms”, Math. Notes, 88:3 (2010), 423–439  mathnet  crossref  crossref  mathscinet  isi
    2. S. A. Gritsenko, “On an additive problem and its application to the problem of distribution of zeros of linear combinations of Hecke $L$-functions on the critical line”, Proc. Steklov Inst. Math., 276 (2012), 90–102  mathnet  crossref  mathscinet  isi
    3. S. A. Gritsenko, D. B. Demidov, “On Zeros of Linear Combinations of Functions of Special Form Related to the Hecke $L$-Functions of Imaginary Quadratic Fields on Short Intervals”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S150–S164  mathnet  crossref  crossref  isi  elib
    4. Rezvyakova I.S., “Selberg'S Method in the Problem About the Zeros of Linear Combinations of l-Functions on the Critical Line”, Dokl. Math., 92:1 (2015), 448–451  mathnet  crossref  mathscinet  zmath  isi  elib
    5. I. S. Rezvyakova, “On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach”, Izv. Math., 80:3 (2016), 602–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. I. S. Rezvyakova, “Additive problem with the coefficients of Hecke $L$-functions”, Proc. Steklov Inst. Math., 296 (2017), 234–242  mathnet  crossref  crossref  mathscinet  isi  elib
    7. 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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