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Zapiski Nauchnykh Seminarov POMI, 1994, Volume 211, Pages 104–119 (Mi znsl5881)  

This article is cited in 2 scientific papers (total in 2 papers)

A shortened equation for convolutions

A. I. Vinogradov

St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Full-text PDF (617 kB) Citations (2)
Abstract: The zeta functions of convolutions are Dirichlet series of the general form $\sum^\infty a_n\cdot n^{-s}$ therefore, they are well convergent in the right half-plane $\operatorname{Re}s>1$. In the critical strip $\operatorname{re}s\in(0,1)$ the convolutions can be represented in terms of the Linnik–Selberg zeta functions whose coefficients are Kloosterman sums. In the present paper, these two representations are combined into a single representation in the same way as the shortened equation for the classical Riemann zeta function. Bibliography: 10 titles.
Received: 14.01.1994
English version:
Journal of Mathematical Sciences, 1997, Volume 83, Issue 5, Pages 626–636
DOI: https://doi.org/10.1007/BF02434849
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: A. I. Vinogradov, “A shortened equation for convolutions”, Problems in the theory of representations of algebras and groups. Part 3, Zap. Nauchn. Sem. POMI, 211, Nauka, St. Petersburg, 1994, 104–119; J. Math. Sci., 83:5 (1997), 626–636
Citation in format AMSBIB
\Bibitem{Vin94}
\by A.~I.~Vinogradov
\paper A shortened equation for convolutions
\inbook Problems in the theory of representations of algebras and groups. Part~3
\serial Zap. Nauchn. Sem. POMI
\yr 1994
\vol 211
\pages 104--119
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5881}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1333877}
\zmath{https://zbmath.org/?q=an:0870.11054}
\transl
\jour J. Math. Sci.
\yr 1997
\vol 83
\issue 5
\pages 626--636
\crossref{https://doi.org/10.1007/BF02434849}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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