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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
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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

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