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Zapiski Nauchnykh Seminarov POMI, 1996, Volume 226, Pages 37–51 (Mi znsl3718)  
This article is cited in 1 scientific paper (total in 1 paper)

Nonhomogeneous Rankin convolutions

A. I. Vinogradov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (1677 kB) Citations (1)
Abstract: The properties of the Rankin convolutions of two eigenfunctions of different parities from the discrete part of the spectrum of the Laplace operator are studied. Analytical continuability of these convolutions into the left half-plane is proved and a functional equation of Riemann type is obtained. Applications to arithmetical convolutions are given. In particular the asymptotics of such convolutions is obtained by using the nonhomogeneous Rankin convolutions. Bibl. 4 titles.
Received: 20.07.1995
English version:
Journal of Mathematical Sciences (New York), 1998, Volume 89, Issue 1, Pages 933–944
DOI: https://doi.org/10.1007/BF02358529
Bibliographic databases:
Document Type: Article
UDC: 511.512
Language: Russian
Citation: A. I. Vinogradov, “Nonhomogeneous Rankin convolutions”, Analytical theory of numbers and theory of functions. Part 13, Zap. Nauchn. Sem. POMI, 226, POMI, St. Petersburg, 1996, 37–51; J. Math. Sci. (New York), 89:1 (1998), 933–944
Citation in format AMSBIB
\Bibitem{Vin96}
\by A.~I.~Vinogradov
\paper Nonhomogeneous Rankin convolutions
\inbook Analytical theory of numbers and theory of functions. Part~13
\serial Zap. Nauchn. Sem. POMI
\yr 1996
\vol 226
\pages 37--51
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3718}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1433345}
\zmath{https://zbmath.org/?q=an:0898.11015|0894.11023}
\transl
\jour J. Math. Sci. (New York)
\yr 1998
\vol 89
\issue 1
\pages 933--944
\crossref{https://doi.org/10.1007/BF02358529}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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