Open Access
Translator Disclaimer
February 2019 Hypertranscendence of the multiple sine function for a complex period
Masaki Kato
Proc. Japan Acad. Ser. A Math. Sci. 95(2): 16-19 (February 2019). DOI: 10.3792/pjaa.95.16

Abstract

It is known that the multiple sine function for a “rational” period satisfies an algebraic differential equation. However, for a non-“rational” period, the differential algebraicity of the multiple sine function is obscure. In this paper, we prove that, if there exists a non-real element in the set $\{\omega_{j}/\omega_{i}|1\leq i<j\leq r\}$, the multiple sine function $\text{Sin}_{r}(x,(\omega_{1},\cdots,\omega_{r}))$ does not satisfy any algebraic differential equation.

Citation

Download Citation

Masaki Kato. "Hypertranscendence of the multiple sine function for a complex period." Proc. Japan Acad. Ser. A Math. Sci. 95 (2) 16 - 19, February 2019. https://doi.org/10.3792/pjaa.95.16

Information

Published: February 2019
First available in Project Euclid: 1 February 2019

zbMATH: 07060334
MathSciNet: MR3905125
Digital Object Identifier: 10.3792/pjaa.95.16

Subjects:
Primary: 11J81 , 11J91 , 33E30

Keywords: algebraic differential equations , hypertranscendence , Multiple sine function

Rights: Copyright © 2019 The Japan Academy

JOURNAL ARTICLE
4 PAGES


SHARE
Vol.95 • No. 2 • February 2019
Back to Top