×

zbMATH — the first resource for mathematics

Limit formulas for multiple Hurwitz zeta functions. (English) Zbl 1444.11187
Summary: We prove the limit formula for the multiple Hurwitz zeta function using absolute zeta functions. These formulas contain Euler’s formula for the Euler constant proved in 1776.

MSC:
11M35 Hurwitz and Lerch zeta functions
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Barnes, E. W., On the theory of the multiple gamma function, Trans. Camb. Philos. Soc., 19, 374-425, (1904)
[2] Deninger, C., Local L-factors of motives and regularized determinants, Invent. Math., 107, 135-150, (1992) · Zbl 0762.14015
[3] Euler, L., De progressionibus harmonicis observationes, Comment. Acad. Scient. Petrop., 7, 150-161, (1740), (Presented March 11, 1734) (Opera Omnia: Series I, Vol. 14, pp. 87-100) [E43]
[4] Euler, L., Evolutio formulae integralis \(\int \partial x(\frac{1}{1 - x} + \frac{1}{l x})\) a termino \(x = 0\) usque ad \(x = 1\) extensae, Nova Acta Acad. Scient. Imp. Petrop., 4, 3-16, (1789), (Presented Feb. 29, 1776) (Opera Omnia, Series I, Vol. 18, pp. 318-334) [E629]
[5] Hasse, H., Ein summierungsverfahren für die riemannsche ζ-reihe, Math. Z., 32, 458-464, (1930) · JFM 56.0894.03
[6] Kurokawa, N.; Koyama, S., Multiple sine functions, Forum Math., 15, 839-876, (2003) · Zbl 1065.11065
[7] Kurokawa, N.; Taguchi, Y., A p-analogue of Euler’s constant and congruence zeta functions, Proc. Japan Acad. Ser. A, 94, 13-16, (2018) · Zbl 1429.11173
[8] Kurokawa, N.; Tanaka, H., Absolute zeta functions and the automorphy, Kodai Math. J., 40, 584-614, (2017) · Zbl 1390.14067
[9] Kurokawa, N.; Tanaka, H., Absolute zeta functions and absolute automorphic forms, J. Geom. Phys., 126, 168-180, (2018), NCG 2017: Connes’ 70th birthday celebration · Zbl 1416.11137
[10] Lerch, M., Další studie v oboru malmsténovských r̆ad, Rozpr. Čes. Akad., 3, 1-61, (1894)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.