On the Mean Value of L-Functions

On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

Liftings and Mean Value Theorems for Automorphic L-functions

A note on the mean value of the zeta and L - functions . XV

The aim of the present note is to develop a unified theory of mean values of automorphic L-functions, albeit what we render here is less explicit and practical than we have desired. This is an outcome of the investigation commenced with the parts XII and XIV, where a framework was laid on the basis of the theory of automorphic representations, and a general approach to the mean values was envis...

A Note on the Mean Value of the Zeta and L-functions. Xiv

The aim of the present note is to develop a study on the feasibility of a unified theory of mean values of automorphic L-functions, a desideratum in the field. This is an outcome of the investigation commenced with the part XII ([13]), where a framework was laid on the basis of the theory of automorphic representations, and a general approach to the mean values was envisaged. Specifically, it i...

On certain mean values and the value-distribution of logarithms of Dirichlet L-functions

We study the value-distribution of Dirichlet L-functions L(s, χ) in the half-plane σ = 1/2. The main result is that a certain average of the logarithm of L(s, χ) with respect to χ, or of the Riemann zeta-function ζ(s) with respect to =s, can be expressed as an integral involving a density function, which depends only on σ and can be explicitly constructed. Several mean-value estimates on L...