Olga Balkanova

Non-vanishing of automorphic L-functions of prime power level

We prove that at the minimum

Moments of L-functions and the Liouville-Green method

25%

Convolution formula for the sums of generalized Dirichlet L-series

25% of L-values associated to holomorphic newforms of fixed even integral weight and large prime power level do not vanish at the critical point.

New error term for the fourth moment of automorphic L-functions

We prove an asymptotic formula for the second moment of primitive L-functions of even weight and prime power level. The error term is estimated uniformly in all parameters: level, weight, shift, and twist.