On Kloosterman sums with multiplicative coefficients

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, $\sqrt{q}(\log q)\ll x⩽q$, $a,b$ are integers, $(a,q)=1$, $e_q(v)=e^{2\pi iv/q}$, $f(n)$ is a multiplicative function, $n{n}^{\ast }\equiv 1(\mathrm{mod}q)$ and the prime sign means that $(n,q)=1$.

13 pages

References in corpus (1)

• Short Kloosterman sums to powerful modulus