IJPAM: Volume 91, No. 4 (2014)

ON SUMMATION OF SUBSERIES OF
THE RIEMANN ZETA FUNCTION

Hongwei Chen
Department of Mathematics
Christopher Newport University
Newport News, VA 23606, USA


Abstract. Three classes of subseries of the Riemann zeta function are evaluated in closed form. All the results are expressed in terms of the Riemann zeta function itself and powers of $\pi$. By using the Euler totient function, we prove that these three classes are unique subseries that exhibit this kind of closed form.

Received: October 8, 2013

AMS Subject Classification: 11M06, 11M35, 11B68, 33B10

Key Words and Phrases: Riemann zeta function, Hurwitz zeta function, Bernoulli polynomials, reflection sums, derivatives of the cotangent.

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DOI: 10.12732/ijpam.v91i4.1 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 4