Mean Value Theorems of Dirichlet Series

Abstract

In this thesis the researcher has proved the 'Mean Value theorems for a class of Dirichlet series' following Ramachandra's method. This method gives simple proof of known results, and infact gives an improvement of Good's result. This thesis consists of two chapters. An approximate functional equation for a class of Dirichlet series is derived; Ramachandra's proof of the Theorem of Montgomery and Vaughan is explained; Proof of the Main theorem and derivations of the results are given; Mean value theorems for two derivatives also is proved; And a brief survey of Zero density estimates is described.