Abstract: The zeta functions are a pillar of number theory. Zeta functions have been objects of great interest for number theorists due to their beauty, mystery, and power. I will discuss this study in the simplest case: the Hurwitz zeta functions. Recently, some surprising direct connections between the special values of Hurwitz zeta functions and power sums were found. In my talk, I will introduce these discoveries. In particular, we will see that special values of Hurwitz zeta functions have some nice integral representations. This is joint work with Jan Minac and Nguyen Duy Tan.