Journal of the Mathematical Society of Japan

Regularizations and finite ladders in multiple trigonometry

Nobushige KUROKAWA and Masato WAKAYAMA

Full-text: Open access

Abstract

We provide an extended interpretation of the zeta regularized product in [D]. This allows us to get regularized product expressions of Hölder's double sine function and its companion, i.e. the double and triple trigonometric functions. The expressions may reasonably explain the ladder structure among these multiple trigonometric functions. We also introduce the notion of finite ladders of functions which helps us understand the meaning behind these regularizations.

Article information

Source
J. Math. Soc. Japan Volume 57, Number 4 (2005), 1197-1216.

Dates
First available in Project Euclid: 14 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1150287310

Digital Object Identifier
doi:10.2969/jmsj/1150287310

Mathematical Reviews number (MathSciNet)
MR2183590

Zentralblatt MATH identifier
1161.11375

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$ 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas

Keywords
Riemann zeta function multiple trigonometric function zeta regularized product Euler-Maclaurin formula Weierstrass canonical form

Citation

KUROKAWA, Nobushige; WAKAYAMA, Masato. Regularizations and finite ladders in multiple trigonometry. J. Math. Soc. Japan 57 (2005), no. 4, 1197--1216. doi:10.2969/jmsj/1150287310. https://projecteuclid.org/euclid.jmsj/1150287310.


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