The Li criterion and the Riemann hypothesis for the Selberg class II

In this paper, we prove an explicit asymptotic formula for the arithmetic formula of the Li coefficients established in Omar and Mazhouda (2007) [10] and Omar and Mazhouda (2010)[11]. Actually, for any function F(s)F(s) in the Selberg class SS, we haveRH⇔λF(n)=dF2nlogn+cFn+O(nlogn), withcF=dF2(γ−1)+12log(λQF2),λ=∏j=1rλj2λj, where γ is the Euler constant.