The critical values of generalizations of the Hurwitz zeta function
Goro ShimuraDepartment of Mathematics Princeton University Princeton NJ 08544-1000 USA
We investigate a few types of generalizations of the Hurwitz zeta function, written in this abstract, where is a complex variable and is a parameter in the domain that depends on the type. In the easiest case we take and one of our main results is that is a constant times for where is the generalized Euler polynomial of degree In another case, is a positive definite real symmetric matrix of size and for is a polynomial function of the entries of of degree We will also define with a totally real number field as the base field, and will show that in a typical case.
Cite this article
Goro Shimura, The critical values of generalizations of the Hurwitz zeta function. Doc. Math. 15 (2010), pp. 489–506DOI 10.4171/DM/303