Shimura, Goro

The critical values of certain Dirichlet series

Doc. Math., J. DMV 13, 775-794 (2008)


Summary: We investigate the values of several types of Dirichlet series $D(s)$ for certain integer values of $s,$ and give explicit formulas for the value $D(s)$ in many cases. The easiest types of $D$ are Dirichlet $L$-functions and their variations; a somewhat more complex case involves elliptic functions. There is one new type that includes $\sum_{n=1}^{\infty} (n^2+1)^{-s}$ for which such values have not been studied previously.

Mathematics Subject Classification

11B68, 11M06, 30B50, 33E05