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We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function ¿(s, a) for s,a¿¿$s, a \\in \\mathbb {C}$, along with an arbitrary number of derivatives with respect to s, to arbitrary precision with rigorous error bounds. Techniques that lead to a fast implementation are discussed. We present new record computations of Stieltjes constants, Keiper-Li coefficients and the first nontrivial zero of the Riemann zeta function, obtained using an open source implementation of the algorithms described in this paper.

Rigorous high-precision computation of the Hurwitz zeta function and its derivatives