Higher Integral Moments of Automorphic L-functions in Short Intervals

Lower Bounds for Moments of Automorphic L-functions over Short Intervals

Let L(s, π) be the principal L-function attached to an irreducible unitary cuspidal automorphic representation π of GLm(AQ). The aim of the paper is to give a simple method to show the lower bounds of mean value for automorphic L-functions over short intervals.

Integral Moments of Automorphic L–functions

We obtain second integral moments of automorphic L–functions on adele groups GL2 over arbitrary number fields, by a spectral decomposition using the structure and representation theory of adele groups GL1 and GL2. This requires complete reformulation of the notion of Poincaré series, replacing the collection of classical Poincaré series over GL2(Q) or GL2(Q(i)) with a single, coherent, global o...

On tensor product $L$-functions and Langlands functoriality

‎In the spirit of the Langlands proposal on  Beyond Endoscopy ‎we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-functions‎. ‎It is well-known that the poles of the $L$-functions have deep impact to the Langlands functoriality‎. ‎Our discussion also‎ ‎includes the meaning of the central value of the tensor product $L$-functions in terms of the Langl...

The prime number theorem in short intervals for automorphic L-functions

Twisted Moments of Automorphic L-functions

We study the moments of the symmetric power L-functions of primitive forms at the edge of the critical strip twisted by the square of the value of the standard L-function at the center of the critical strip. We give a precise expansion of the moments as the order goes to infinity. CONTENTS