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Zap. Nauchn. Sem. LOMI, 1978, Volume 76, Pages 159–166 (Mi znsl1937)  

Spectral methods in arithmetic problems

N. V. Kuznetsov


Abstract: Combining ideas of convolution due to Rankin with spectral considerations of Selberg, the author proposes a new approach to obtaining mean values for certain number-theoretic functions $f(n)$. This approach is illustrated for the examples of functions $f(n)=\tau(Mn^2+N)$, $\tau(n)\tau(Mn+N)$, where $\tau(n)$ is the number of divisors of $n$.

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English version:
Journal of Soviet Mathematics, 1982, 18:3, 398–404

Bibliographic databases:

UDC: 511.3, 517.43, 519.45

Citation: N. V. Kuznetsov, “Spectral methods in arithmetic problems”, Analytical theory of numbers and theory of functions, Zap. Nauchn. Sem. LOMI, 76, "Nauka", Leningrad. Otdel., Leningrad, 1978, 159–166; J. Soviet Math., 18:3 (1982), 398–404

Citation in format AMSBIB
\Bibitem{Kuz78}
\by N.~V.~Kuznetsov
\paper Spectral methods in arithmetic problems
\inbook Analytical theory of numbers and theory of functions
\serial Zap. Nauchn. Sem. LOMI
\yr 1978
\vol 76
\pages 159--166
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1937}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=527794}
\zmath{https://zbmath.org/?q=an:0476.10040|0419.10043}
\transl
\jour J. Soviet Math.
\yr 1982
\vol 18
\issue 3
\pages 398--404
\crossref{https://doi.org/10.1007/BF01084849}


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