Values of \(L\)-series of Hecke eigenforms (Q2308825)

In the paper under review, the authors determine a formula for the average values of \(L\)-series associated to eigenforms at complex values. More precisely, they evaluate the integral \( \gamma_k(s)^{-1} \int_{0}^{\infty} R_{s,k}(it) t^{s'-1} dt \) in terms of Gamma function, Riemann zeta function and the hypergeometric series under some conditions on \(s\) and \(s'\). Here \(R_{s,k}\) is the kernel function on the modular group.