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