Article
Keywords:
Lerch’s formula; Hurwitz zeta function; zeta regularized product
Summary:
We give higher-power generalizations of the classical Lerch formula for the gamma function.
References:
[1] S. Bochner:
Zeta functions and Green’s functions for linear partial differential operators of elliptic type with constant coefficients. Ann. Math. 57 (1953), 32–56.
DOI 10.2307/1969725 |
MR 0054830 |
Zbl 0050.08001
[3] N. Kurokawa:
Gamma factors and Plancherel measures. Proc. Japan Acad. 68A (1992), 256–260.
MR 1202627 |
Zbl 0797.11053
[5] N. Kurokawa and M. Wakayama:
Generalized zeta regularizations, quantum class number formulas, and Appell’s $O$-functions. The Ramanujan J (to appear).
MR 2193381
[6] M. Lerch: Další studie v oboru Malmsténovských řad. Rozpravy České Akad. věd 3 (1894), 1–61.
[7] Yu. I. Manin:
Lectures on zeta functions and motives (according to Deninger and Kurokawa). Astérisque 228 (1995), 121–163.
MR 1330931