ON SOME NUMBER THEORETIC SUM

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详细

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.

作者简介

V. Iudelevich

Lomonosov Moscow State University

Moscow, Russia

参考

  1. Хооли K. Применение методов решета в теории чисел. М.: Наука, 1987.
  2. Korolev M.A. On Karatsuba’s problem concerning the divisor function // Monatsh. Math. (168). 2012. P. 403-441.
  3. Fouvry E., Radziwill M. Level of distribution of unbalanced convolutions // Ann. scient. de l’Ecole Normale Superieure (55). 2022. P. 537-568.
  4. Bettin S., Chandee V. Trillinear forms with Kloosterman fractions // Adv. in Math. (328). 2018. P. 1234-1262.

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