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ON SOME NUMBER THEORETIC SUM
- Authors: Iudelevich V.V1
-
Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 521 (2025)
- Pages: 38-42
- Section: MATHEMATICS
- URL: https://rjeid.com/2686-9543/article/view/683150
- DOI: https://doi.org/10.31857/S2686954325010066
- EDN: https://elibrary.ru/BTKGUJ
- ID: 683150
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Abstract
We obtain an asymptotic formula for the sum Q(x) = ∑n≤x/r(n+1)≠0 r(n)/r(n+1), (x → +∞), where r(n) denotes the number of representations of n as a sum of two squares.
References
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- Korolev M.A. On Karatsuba’s problem concerning the divisor function // Monatsh. Math. (168). 2012. P. 403-441.
- Fouvry E., Radziwill M. Level of distribution of unbalanced convolutions // Ann. scient. de l’Ecole Normale Superieure (55). 2022. P. 537-568.
- Bettin S., Chandee V. Trillinear forms with Kloosterman fractions // Adv. in Math. (328). 2018. P. 1234-1262.
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