Analysis of the nontrivial zeros for the certain Dirichlet $L$-series

Abstract

In the present paper we propose a new approach for the generalized Riemann hypothesis in theoretical framework of the Dirichlet $L$-series. The Dirichlet’s lambda function is used as the testing function to prove the generalized Riemann hypothesis. The obtained results can be also applied to consider the other classes of the Dirichlet $L$-series.