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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2025, Volume 521, Pages 38–42
DOI: https://doi.org/10.31857/S2686954325010066 (Mi danma618) 		 
MATHEMATICS

On some number theoretic sum

V. V. Iudelevich

Lomonosov Moscow State University
DOI: https://doi.org/10.31857/S2686954325010066
Abstract: We obtain an asymptotic formula for the sum $Q(x) = \sum_{n\leq x/r(n+1)\neq0}\frac{r(n)}{r(n+1)}$, $(x \to +\infty)$, where $r(n)$ denotes the number of representations of $n$ as a sum of two squares.
Keywords: a sum of two squares, Dirichlet’s characters, the large sieve inequality, the dispersion method.
Funding agency Grant number
Nonprofit foundation for support of young scientists "Möbius Contest"
This work was supported by the August Möbius Contest Foundation for supporting young scientists.
Presented: A. L. Semenov
Received: 09.04.2024
Revised: 03.12.2024
Accepted: 03.12.2024
English version:
Doklady Mathematics, 2025, Volume 111, Issue 1, Pages 25–28
DOI: https://doi.org/10.1134/S1064562424601586
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. V. Iudelevich, “On some number theoretic sum”, Dokl. RAN. Math. Inf. Proc. Upr., 521 (2025), 38–42; Dokl. Math., 111:1 (2025), 25–28
Citation in format AMSBIB
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\by V.~V.~Iudelevich
\paper On some number theoretic sum
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2025
\vol 521
\pages 38--42
\mathnet{http://mi.mathnet.ru/danma618}
\elib{https://elibrary.ru/item.asp?id=80559505}
\transl
\jour Dokl. Math.
\yr 2025
\vol 111
\issue 1
\pages 25--28
\crossref{https://doi.org/10.1134/S1064562424601586}
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