Moment Of Automorphic L-functions Research Articles

The cubic moment of automorphic L-functions in the weight aspect

We prove an explicit formula for the cubic moment of central values of automorphic L-functions associated to primitive cusp forms of level one and large weight. The resulting explicit formula contains the main term predicted by the random matrix theory conjectures, while the error term is expressed as the fourth moment of the Riemann zeta function weighted by the F23 hypergeometric function. As a corollary, we derive a new upper bound for the cubic moment improving the previous result of Peng. Furthermore, we obtain a new subconvexity estimate for automorphic L-functions in the weight aspect.

Integral moments of automorphic L-functions

Let [Formula: see text] be a self-contragredient irreducible unitary cuspidal representation of [Formula: see text] with [Formula: see text], and [Formula: see text] be the automorphic [Formula: see text]-function attached to [Formula: see text]. Assume that [Formula: see text] is self-contragredient. Under the Generalized Ramanujan Conjecture and Generalized Riemann Hypothesis for [Formula: see text], the estimate [Formula: see text] holds for all real number [Formula: see text] as [Formula: see text].

Fractional moments of automorhic L-FUNCTIONS. II

Asymptotics for fractional moments of automorphic L-functions are found. Bibliography: 11 titles.

Fractional moments of automorphic L-functions on GL(m)

Let π be an irreducible unitary cuspidal representation of \(GL_m \left( {\mathbb{A}_\mathbb{Q} } \right)\), m ≥ 2. Assume that π is self-contragredient. The author gets upper and lower bounds of the same order for fractional moments of automorphic L-function L(s, π) on the critical line under Generalized Ramanujan Conjecture; the upper bound being conditionally subject to the truth of Generalized Riemann Hypothesis.