A criterion for the Generalized Riemann hypothesis

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

“…The generalized Riemann hypothesis can be connected with the Goldbach's conjecture [20] and the Diophantine equations [21], and is one of the important problems in the mathematics [17]. The criterion [22] and the number of zeros and poles for the Dirichlet L-series [23], hybrid bounds [24] and related functions [25,26] were reported. As one of the classes of the Dirichlet L-series, the Dirichlet's lambda function λ (s) can be expressed as follows:…”