The sixth moment of automorphic L-functions

The Cubic Moment of Central Values of Automorphic L-functions

A Note on the Second Moment of Automorphic L-functions

We obtain the formula for the twisted harmonic second moment of the L-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean value theorem is reminiscent of recent results of Conrey and Young on the reciprocity formula for the twisted second moment of Dirichlet L-functions.

The Sixth Power Moment of Dirichlet L-functions

Understanding moments of families of L-functions has long been an important subject with many number theoretic applications. Quite often, the application is to bound the error term in an asymptotic expression of the average of an arithmetic function. Also, a good bound for a moments can be used to obtain a point-wise bound for an individual L-function in the family; strong enough bounds of this...

The Reciprocity Law for the Second Moment of Automorphic L-functions

where A and B are some explicit constants. This provides an asymptotic formula for M(p, q) − √ p/qM(−q, p) under the condition that p ≪ q2/3−ε. The error term above was improved by Young [6] so that the asymptotic formula holds for p ≪ q1−ε. In this paper, we consider the twisted moments of the families of L-functions arising from S∗ 2 (p) and S∗ 2 (q), the sets of primitive Hecke eigenforms of...

Lectures on automorphic L-functions

PREFACE This article follows the format of five lectures that we gave on automorphic Lfunctions. The lectures were intended to be a brief introduction for number theorists to some of the main ideas in the subject. Three of the lectures concerned the general properties of automorphic L-functions, with particular reference to questions of spectral decomposition. We have grouped these together as ...