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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 1, Pages 63–91 (Mi izv1632)  

This article is cited in 18 scientific papers (total in 20 papers)

On the zeros of some Dirichlet series lying on the critical line

S. M. Voronin

Abstract: A linear combination of Dirichlet $L$-functions which are known not to have an Euler product is considered. It is proved that the interval
$$ [\frac12-iT,\frac12+iT] $$
contains for an arbitrary constant $c>0$ more than $cT$ zeros for $T\to\infty$.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:1, 55–82

Bibliographic databases:

UDC: 511
MSC: Primary 10H10; Secondary 10H08
Received: 05.06.1979

Citation: S. M. Voronin, “On the zeros of some Dirichlet series lying on the critical line”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980), 63–91; Math. USSR-Izv., 16:1 (1981), 55–82

Citation in format AMSBIB
\by S.~M.~Voronin
\paper On the zeros of some Dirichlet series lying on the critical line
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 1
\pages 63--91
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 1
\pages 55--82

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    This publication is cited in the following articles:
    1. A. A. Karatsuba, “On the zeros of the Davenport–Heilbronn function lying on the critical line”, Math. USSR-Izv., 36:2 (1991), 311–324  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Karatsuba, “Zeros of certain Dirichlet series”, Russian Math. Surveys, 45:1 (1990), 207–208  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. A. Karatsuba, “On the zeros of a special type of function connected with Dirichlet series”, Math. USSR-Izv., 38:3 (1992), 471–502  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. S. A. Gritsenko, “Zeros of linear combinations of functions of a special type that are connected with Selberg Dirichlet series”, Izv. Math., 60:4 (1996), 655–694  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. S. A. Gritsenko, “Zeros of special form of functions related to Dirichlet series from the Selberg class”, Math. Notes, 60:4 (1996), 449–453  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. S. A. Gritsenko, “Zeros of a special type of function associated with Hecke $L$-functions of imaginary quadratic fields”, Izv. Math., 61:1 (1997), 45–68  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. G. I. Arkhipov, V. I. Blagodatskikh, A. A. Bolibrukh, V. A. Iskovskikh, A. A. Karatsuba, Yu. V. Prokhorov, A. T. Fomenko, V. N. Chubarikov, I. R. Shafarevich, “Sergei Mikhailovich Voronin (obituary)”, Russian Math. Surveys, 53:4 (1998), 777–781  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. 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
    9. S. A. Gritsenko, “On a Problem of Karatsuba”, Math. Notes, 88:4 (2010), 492–502  mathnet  crossref  crossref  mathscinet  isi
    10. I. S. Rezvyakova, “Zeros of linear combinations of Hecke $L$-functions on the critical line”, Izv. Math., 74:6 (2010), 1277–1314  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. E. Bombieri, A. Ghosh, “Around the Davenport–Heilbronn function”, Russian Math. Surveys, 66:2 (2011), 221–270  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. 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  elib  elib
    13. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22  mathnet  crossref  crossref  zmath  isi  elib
    14. 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
    15. A. A. Karatsuba, “Venskii doklad: o kolichestve nulei dzeta-funktsii Rimana na korotkikh promezhutkakh kriticheskoi pryamoi”, Chebyshevskii sb., 16:1 (2015), 19–31  mathnet  elib
    16. Do Dyk Tam, “Raspredelenie nulei, lezhaschikh na kriticheskoi pryamoi, lineinykh kombinatsii $L$-funktsii Dirikhle”, Chebyshevskii sb., 16:3 (2015), 183–208  mathnet  elib
    17. 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  isi
    18. 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
    19. S. A. Gritsenko, “On the Zeros of the Davenport–Heilbronn Function Lying on the Critical Line”, Math. Notes, 101:1 (2017), 166–170  mathnet  crossref  crossref  mathscinet  isi  elib
    20. 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
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