New estimates of double trigonometric sums with exponential functions

We establish a new bound for the exponential sum x∈X y∈Y γ(y) exp(2πiaλ xy /p) , where λ is an element of the residue ring modulo a large prime number p, X and Y are arbitrary subsets of the residue ring modulo p − 1 and γ(n) are any complex numbers with |γ(n)| ≤ 1. In particular, we improve several previously known bounds.