Without summing over characters, one gets the p-adic Hurwitz version, and the regular Hurwitz version is a factor in the sum for an L-series.
Without summing over characters, one gets the p-adic Hurwitz version, and the regular Hurwitz version is a factor in the sum for an L-series. When defined over an algebraic variety, the Hasse-Weil version results, while if this function is represented by summing over ideals, the Dedekind version is obtained. In its most common incarnation, this function's reciprocal produces the Mobius mu function, and it has a functional equation relating its value at s to the value at 1 minus s. That most common version also may or may not have any nontrivial roots with real part not equal to one half, a namesake hypothesis. FTP, name these mathematical entities, the most famous of which sums 1 over n to the s and is named for Riemann.
Without summing over characters, one gets the p-adic Hurwitz version, and the regular Hurwitz version is a factor in the sum for an L-series.
{zeta} functions (accept Dirichlet {L-function} before (*))