THE RAMANUJAN JOURNAL, Vol. 10, No. 3 (2005),
Generalized Zeta Regularizations, Quantum Class Number, and Appel's $0$-Functions
Received July 30, 2002; Accepted October 8, 2002
Abstract. We introduce a generalized notion of zeta regularization. As applications we show the quantum analogue of the Lerch formula and of the Dirichlet class number formulas. We also give further examples related to Appel's $0$-functions.
Keywords: zeta regularization, Hurwitz zeta function, quantum class number, Appell's $O$-function, $q$-gamma function
2000 Mathematics Classification: Primary 11M36
Original article available at www.springerlink.com:
Sat Jul 8 10:50:55 EDT 2006