Publication Date


Advisor(s) - Committee Chair

Dr. Dominic Lanphier (Director), Dr. Tilak Bhattacharya, Dr. Claus Ernst


Dominic Lanphier, in the Addendum, reviews some results of Stieltjes constants and relates them to the thesis. Mark Coffey is thanked for bringing attention to this work.

Degree Program

Department of Mathematics and Computer Science

Degree Type

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

AddendumStieltjesConstants 201120.pdf (171 kB)
Addendum to Higher Derivatives of the Hurwitz Zeta Function

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