New estimates of double trigonometric sums with exponential functions

Abstract

We establish a new bound for the exponential sum \begin{eqnarray*} \sum_{x\in\mathcal{X}}\Big|\sum_{y\in \mathcal{Y}}γ(y)\exp(2πi a λ^{xy}/p)\Big|, \end{eqnarray*} where $\lambda$ is an element of the residue ring modulo a large prime number $p,$ $\mathcal{X}$ and $\mathcal{Y}$ are arbitrary subsets of the residue ring modulo $p-1$ and $\gamma (n)$ are any complex numbers with $|\gamma (n)|\le 1.$ In particular, we improve several previously known bounds.

10 pages

References in corpus (1)

• On a symmetric congruence and its applications