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Zapiski Nauchnykh Seminarov LOMI, 1981, Volume 109, Pages 41–82 (Mi znsl3919)  

This article is cited in 3 scientific papers (total in 3 papers)

Analogues of the Gauss–Vinogradov formula on the critical line

A. I. Vinogradov, L. A. Takhtadzhyan
Abstract: An asymptotic behavior of the sum $\sum_{p\equiv v(\operatorname{mod}4),\ p\le X}L(s,\chi_p)$ for $X\to\infty$ is studied in the critical strip, where $L(s,\chi_p)$ is the Dirichlet series with the quadratic character $\chi_p$ modulo $p$, where $p$ is a prime number; $v=1$ or $3$. With the help of large seive estimates a formula for this sum is obtained with two asymptotic terms on the critical line of the variable $s$. As a corollary the asymptotic expansion of this sum at the point $s=1/2$ is presented. The asymptotic formula for the sum $\sum_{|d|\le X}L(s,\chi_d)$, where $d$ runs over discriminants of quadratic fields, is also obtained.
English version:
Journal of Soviet Mathematics, 1984, Volume 24, Issue 2, Pages 183–208
DOI: https://doi.org/10.1007/BF01087241
Bibliographic databases:
Document Type: Article
UDC: 511.33+511.43
Language: Russian
Citation: A. I. Vinogradov, L. A. Takhtadzhyan, “Analogues of the Gauss–Vinogradov formula on the critical line”, Differential geometry, Lie groups and mechanics. Part IV, Zap. Nauchn. Sem. LOMI, 109, "Nauka", Leningrad. Otdel., Leningrad, 1981, 41–82; J. Soviet Math., 24:2 (1984), 183–208
Citation in format AMSBIB
\Bibitem{VinTak81}
\by A.~I.~Vinogradov, L.~A.~Takhtadzhyan
\paper Analogues of the Gauss--Vinogradov formula on the critical line
\inbook Differential geometry, Lie groups and mechanics. Part~IV
\serial Zap. Nauchn. Sem. LOMI
\yr 1981
\vol 109
\pages 41--82
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl3919}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=629115}
\zmath{https://zbmath.org/?q=an:0534.10039|0468.10023}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 24
\issue 2
\pages 183--208
\crossref{https://doi.org/10.1007/BF01087241}
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  • https://www.mathnet.ru/eng/znsl/v109/p41
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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