Abstract

Moments of families of L-functions provide understanding of their size and also about their distribution. The aim of this thesis is to calculate the asymptotics of the first moment of L-functions associated to primitive cubic Hecke characters over $Q(\omega)$ and upper bounds for 2k-th moments for the same family. Both of these results assume Generalized Riemann Hypothesis. We consider the full family of characters which results in a main term of order x log x. We also calculate conditional upper bounds for 2k-th moments for the same family and conclude that there >> x primitive characters of conductor at most x for which the L-function doesn't vanish at the central point.