Type: Article

Exponential sums with Catalan numbers and middle binomial coefficients

Moubariz Z. Garaev; Florian Luca; Igor E. Shparlinski;

Abstract:

We estimate the number of solutions of certain congruences with Catalan numbers and middle binomial coefficients modulo a prime. We use these results to bound double exponential sums with products of two Catalan numbers and two middle binomial coefficients, respectively, which in turn lead us to upper bounds on single exponential sums.