| Title:
|
A generalization of Lerch’s formula (English) |
| Author:
|
Kurokawa, Nobushige |
| Author:
|
Wakayama, Masato |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
941-947 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give higher-power generalizations of the classical Lerch formula for the gamma function. (English) |
| Keyword:
|
Lerch’s formula |
| Keyword:
|
Hurwitz zeta function |
| Keyword:
|
zeta regularized product |
| MSC:
|
11M35 |
| MSC:
|
11M36 |
| MSC:
|
33B15 |
| idZBL:
|
Zbl 1114.11074 |
| idMR:
|
MR2100006 |
| . |
| Date available:
|
2009-09-24T11:19:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127942 |
| . |
| Reference:
|
[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. Zbl 0050.08001, MR 0054830, 10.2307/1969725 |
| Reference:
|
[2] Ch. Deninger: Local $L$-factors of motives and regularized determinants.Invent. math. 107 (1992), 135–150. Zbl 0762.14015, MR 1135468, 10.1007/BF01231885 |
| Reference:
|
[3] N. Kurokawa: Gamma factors and Plancherel measures.Proc. Japan Acad. 68A (1992), 256–260. Zbl 0797.11053, MR 1202627 |
| Reference:
|
[4] N. Kurokawa and M. Wakayama: Higher Selberg zeta functions.Commun. Math. Phys. 247 (2004), 447–466. MR 2063268, 10.1007/s00220-004-1065-z |
| Reference:
|
[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 |
| Reference:
|
[6] M. Lerch: Další studie v oboru Malmsténovských řad.Rozpravy České Akad. věd 3 (1894), 1–61. |
| Reference:
|
[7] Yu. I. Manin: Lectures on zeta functions and motives (according to Deninger and Kurokawa).Astérisque 228 (1995), 121–163. MR 1330931 |
| . |
