Advisor(s) - Committee Chair
Dr. Dominic Lanphier (Director), Dr. Tilak Bhattacharya, Dr. Claus Ernst
Department of Mathematics and Computer Science
Master of Science
The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have been studied by several mathematicians. Apostol in particular gave a computable formula for the values of the derivatives of ζ(s) at s = 0. The Hurwitz zeta function ζ(s,q) is a generalization of ζ(s). We modify Apostolʼs methods to find values of the derivatives of ζ(s,q) with respect to s at s = 0. As a consequence, we obtain relations among certain important constants, the generalized Stieltjes constants. We also give numerical estimates of several values of the derivatives of ζ(s,q).
Mathematics | Number Theory
Musser, Jason, "Higher Derivatives of the Hurwitz Zeta Function" (2011). Masters Theses & Specialist Projects. Paper 1093.