On the Dirichlet Eta Function

[摘要] We know that the Riemann zeta function ζ is the analytic functionof the complex variable s, defined in the half-plane R(s) >1 by Sarnak where the series s n−∑ is absolutely convergent for R(s)>1 and theproduct ∏(1-p-s)-1 extends over all the prime numbers p∊P={2,3,5,7,…}and as shown by Riemann, ζ can be continued analytically to \{1} asa meromorphic function and has a simple pole at s=1 with residue 1[2].

[关键词] Dirichlet eta function;Riemann zeta function;Complex variable