Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T13:32:11.541Z Has data issue: false hasContentIssue false
  • English
  • Français

Some arithmetical consequences of Jacobi's triple product identity

Published online by Cambridge University Press:  01 November 1997

DANIEL DUVERNEY
DANIEL DUVERNEY
Affiliation:
24, Place du Concert, F-59800 Lille, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to prove irrationality results from Jacobi's triple product identity, which can be written, for x∈[Copf]*, y∈[Copf], [mid ]y[mid ]<1:

formula here

There are various proofs of this identity; the classical one rests on the theory of theta functions ([3], theorem 6, p. 69). An alternative proof uses Heine's summation formula ([10], p. 12). An elementary, self-contained proof, can be found in [9], p. 227.

In this paper, we will use the same elementary methods as in [5] and [6], and prove the following theorems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 3 , November 1997 , pp. 393 - 399
Copyright
Cambridge Philosophical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)