Year: 2017
Type: article
Abstract: The series of some new estimates for the sums of the type \[ S_{q}(x;f)\,=\,\mathop{{\sum}'}\limits_{n\leqslant x}f(n)e_{q}(an^{*}+bn) \] is obtained. Here $q$ is a sufficiently large integer, $\sqrt{q}(\log{q})\!\ll\!x\leqslant q$, $a,b$ are integers, $(a,q)=1$, $e_{q}(v) = e^{2πiv/q}$, $f(n)$ is a multiplicative function, $nn^{*}\equiv 1 \pmod{q}$ and the prime sign means that $(n,q)=1$.
Source: Izvestiya Mathematics
DOI: 10.1070/im8633
Author: M. A. Korolev
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4755196281
OpenAlex ID: W2540610552