Abstract

A limit theorem in the sense of weak convergence of probability measures on the complex plane for twisted with Dirichlet character L-functions of holomorphic normalized Hecke eigen cusp forms with an increasing modulus of the character is proved.

Highlights

  • Let q ∈ N, and let χ(m) denote a Dirichlet character modulo q

  • The aim of this note is a generalization to the space (C, B(C)) of limit theorems with an increasing prime modulus q for |L(s, F, χ)| and arg L(s, F, χ)

  • Substituting this in (5), we find that aτ,k(m) ms

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Summary

Introduction

Let q ∈ N, and let χ(m) denote a Dirichlet character modulo q. A. Kolupayeva where χ0 denotes the principal character mod q. Where in place of dots a condition satisfied by a pair (q, χ(mod q)) is to be written. The aim of this note is a generalization to the space (C, B(C)) of limit theorems with an increasing prime modulus q for |L(s, F, χ)| and arg L(s, F, χ) (see, [3] and [4], respectively).

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