Scott Kirila

Discrete moments of Dirichlet L-functions

Discrete moments were first studied by Gonek in 1984, who derived a (conditional) asymptotic formula for the second moment of the derivative of the Riemann zeta function.

In general, discrete moments of L-functions largely resemble their continuous analogue, and much work has been done in taking results from the latter setting and translating them to the former. However, there are typically obstacles which are unique to the discrete setting. We discuss upper bounds for discrete moments of Dirichlet L-functions and how Adam Harper's (continuous) method applies, paying particular attention to one such obstacle arising from Landau's formula.