Some Applications of Laplace Transforms in Analytic Number Theory

In this overview paper, presented at the meeting DANS14, Novi Sad, July3-7, 2014, we give some applications of Laplace transforms to analytic number theory. These include the classical circle and divisor problem, moments of $|\zeta(1/2+it)|$, and a discussion of two functional equations connected to a work of Prof. Bogoljub Stankovi\'c.Comment: 15 page