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

The Fourth Power Moment of Automorphic L-functions for Gl(2) over a Short Interval

In this paper we will prove bounds for the fourth power moment in the t aspect over a short interval of automorphic L-functions L(s, g) for GL(2) on the central critical line Re s = 1/2. Here g is a fixed holomorphic or Maass Hecke eigenform for the modular group SL2(Z), or in certain cases, for the Hecke congruence subgroup Γ0(N ) with N > 1. The short interval is from a large K to K + K103/13...

Mollification of the fourth moment of automorphic L-functions and arithmetic applications

In this paper, we compute the twisted fourth power moment of modular L-functions of prime level near the critical line. This allows us to prove some new non-vanishing results on the central values of automorphic L-functions, in particular whose obtained by base change from GL2(Q) to GL2(K) for K a cyclic field of low degree.

The Fourth Moment of Dirichlet L-functions

for certain explicitly computable constants ai. The difficult part of extending Ingham’s result to include the lower-order terms is asymptotically evaluating the off-diagonal terms. The family of all primitive Dirichlet L-functions of modulus q is similar in some ways to the Riemann zeta function in t-aspect, but is more difficult to analyze. In 1981, Heath-Brown obtained an asymptotic formula ...

The Fourth Moment of Dirichlet L-functions

Here ∑∗ denotes summation over primitive characters χ (mod q), φ(q) denotes the number of primitive characters (mod q), and ω(q) denotes the number of distinct prime factors of q. Note that φ(q) is a multiplicative function given by φ(p) = p − 2 for primes p, and φ(p) = p(1 − 1/p) for k ≥ 2 (see Lemma 1 below). Also note that when q ≡ 2 (mod 4) there are no primitive characters (mod q), and so ...

The Cubic Moment of Central Values of Automorphic L-functions