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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 $T\to\infty$.
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Mathematics of the USSR-Izvestiya, 1981, 16:1, 55–82
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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
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\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 1
\pages 55--82
\crossref{https://doi.org/10.1070/IM1981v016n01ABEH001296}
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http://mi.mathnet.ru/eng/izv1632 http://mi.mathnet.ru/eng/izv/v44/i1/p63
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This publication is cited in the following articles:
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A. A. Karatsuba, “On the zeros of the Davenport–Heilbronn function lying on the critical line”, Math. USSR-Izv., 36:2 (1991), 311–324
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A. A. Karatsuba, “Zeros of certain Dirichlet series”, Russian Math. Surveys, 45:1 (1990), 207–208
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A. A. Karatsuba, “On the zeros of a special type of function connected with Dirichlet series”, Math. USSR-Izv., 38:3 (1992), 471–502
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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
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S. A. Gritsenko, “Zeros of special form of functions related to Dirichlet series from the Selberg class”, Math. Notes, 60:4 (1996), 449–453
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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
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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
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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
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S. A. Gritsenko, “On a Problem of Karatsuba”, Math. Notes, 88:4 (2010), 492–502
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I. S. Rezvyakova, “Zeros of linear combinations of Hecke $L$-functions on the critical line”, Izv. Math., 74:6 (2010), 1277–1314
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E. Bombieri, A. Ghosh, “Around the Davenport–Heilbronn function”, Russian Math. Surveys, 66:2 (2011), 221–270
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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
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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
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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
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A. A. Karatsuba, “Venskii doklad: o kolichestve nulei dzeta-funktsii Rimana na korotkikh promezhutkakh kriticheskoi pryamoi”, Chebyshevskii sb., 16:1 (2015), 19–31
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Do Dyk Tam, “Raspredelenie nulei, lezhaschikh na kriticheskoi pryamoi, lineinykh kombinatsii $L$-funktsii Dirikhle”, Chebyshevskii sb., 16:3 (2015), 183–208
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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
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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
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S. A. Gritsenko, “On the Zeros of the Davenport–Heilbronn Function Lying on the Critical Line”, Math. Notes, 101:1 (2017), 166–170
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S. A. Gritsenko, “On the zeros of the Davenport–Heilbronn function”, Proc. Steklov Inst. Math., 296 (2017), 65–87
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