17 - Critical Zeros of GL(2) L-Functions

Abstract

This chapter describes the critical zeros of GL (2) L-functions. The last group of the Riemann zeta-function is subdivided into L-series arising from holomorphic cusp forms and those arising from real-analytic cusp forms, that is, the maass wave forms. In these cases, it is assumed that the cusp forms are Hecke Eigen forms. These cases arise from modular forms. The chapter presents an outline of a proof, that is, the basic ingredients common to three cases. It discusses the differences between the actual implementation of the method in the various known cases. The Riemann Hypothesis is formulated to allow for zeros off the line but on the real axis.