Dmitry Frolenkov

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

We prove that at the minimum

Bounds for a spectral exponential sum: BOUNDS FOR A SPECTRAL EXPONENTIAL SUM

25\%

Moments of L-functions and the Liouville-Green method

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.

Bounds for the spectral exponential sum

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.

Convolution formula for the sums of generalized Dirichlet L-series

We prove new upper bounds for the spectral exponential sum by refining the process by which one evaluates mean values of

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

L

Convolution formula for the sums of generalized Dirichlet L-functions.

-functions multiplied by an oscillating function. In particular, we introduce a method which is capable of taking into consideration the oscillatory behaviour of the function. This gives an improvement of the result of Luo and Sarnak when

Sums of Kloosterman sums in the prime geodesic theorem.

T\geq X^{1/6+2\theta/3}