Journal of the Mathematical Society of Japan

Regularizations and finite ladders in multiple trigonometry

Nobushige KUROKAWA and Masato WAKAYAMA

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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.

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

First available in Project Euclid: 14 June 2006

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Zentralblatt MATH identifier

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

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


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.

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