i will talk about two problems, completely different from each other and both quite fun, that turn out to be related to the riemann hypothesis. one of them concerns the universal limiting position (after rescaling) of the zeros of polynomials belonging to a rather general class, with as an application a weak version of an old conjecture of polya that in its strong version would imply the riemann hypothesis. the other gives an equivalence between the generalized riemann hypothesis and a statement about the growth rate of the determinants of certain matrices whose entries are elementary cotangent sums, with an unexpected appearance of quantum modular forms as a byproduct.