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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 3, Pages 483–514 (Mi izv997)  

This article is cited in 13 scientific papers (total in 14 papers)

On the zeros of a special type of function connected with Dirichlet series

A. A. Karatsuba


Abstract: Theorems are proved on the number of zeros of linear combinations of Dirichlet $L$-functions that lie on intervals of the critical line.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 38:3, 471–502

Bibliographic databases:

UDC: 511
MSC: Primary 11M26, 11M41; Secondary 11M35, 11R42
Received: 27.12.1990

Citation: A. A. Karatsuba, “On the zeros of a special type of function connected with Dirichlet series”, Izv. Akad. Nauk SSSR Ser. Mat., 55:3 (1991), 483–514; Math. USSR-Izv., 38:3 (1992), 471–502

Citation in format AMSBIB
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\vol 55
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\pages 483--514
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\jour Math. USSR-Izv.
\yr 1992
\vol 38
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\pages 471--502
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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. A. A. Karatsuba, “On the number of zeros of the Riemann zeta-function lying in almost all short intervals of the critical line”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 353–376  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Karatsuba, “A refinement of theorems on the number of zeros lying on intervals of the critical line of certain Dirichlet series”, Russian Math. Surveys, 47:2 (1992), 219–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. A. Karatsuba, “On the zeros of arithmetic Dirichlet series without Euler product”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 193–203  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. S. A. Gritsenko, “Approximate functional equation for the product of two Dirichlet $L$-functions”, Russian Acad. Sci. Izv. Math., 45:2 (1995), 255–280  mathnet  crossref  mathscinet  zmath  isi
    5. 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
    6. A. A. Karatsuba, “Fractional Moments and Zeros of $\zeta (s)$ on the Critical Line”, Math. Notes, 72:4 (2002), 466–472  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. S. A. Gritsenko, “On a Problem of Karatsuba”, Math. Notes, 88:4 (2010), 492–502  mathnet  crossref  crossref  mathscinet  isi
    8. 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
    9. 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
    10. Do Dyk Tam, “Raspredelenie nulei, lezhaschikh na kriticheskoi pryamoi, lineinykh kombinatsii $L$-funktsii Dirikhle”, Chebyshevskii sb., 16:3 (2015), 183–208  mathnet  elib
    11. Do Dyk Tam, “O kolichestve nulei dzeta-funktsii Rimana, lezhaschikh v «pochti vsekh» ochen korotkikh promezhutkakh okrestnosti kriticheskoi pryamoi”, Chebyshevskii sb., 17:3 (2016), 106–124  mathnet  elib
    12. A. A. Karatsuba, “On zeros of certain Dirichlet series”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 6–10  mathnet  crossref  crossref  isi  elib
    13. 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  mathscinet  isi  elib  elib
    14. S. A. Gritsenko, “O drobnykh momentakh uspokoennykh $L$-funktsii Lirikhle”, Chebyshevskii sb., 18:4 (2017), 168–187  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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