New estimates of double trigonometric sums with exponential functions

M. Z. Garaev, A. A. Karatsuba

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…