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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2025 Volume 521, Pages 38–42 (Mi danma618)

MATHEMATICS

On some number theoretic sum

V. V. Iudelevich

Lomonosov Moscow State University

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.

UDC: 517.54

Presented: A. L. Semenov
Received: 09.04.2024
Revised: 03.12.2024
Accepted: 03.12.2024

DOI: 10.31857/S2686954325010066



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© Steklov Math. Inst. of RAS, 2025