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ARITHMETIC PROPERTIES OF INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS

Part of: Diophantine approximation, transcendental number theory Differential and difference algebra

Published online by Cambridge University Press:  08 January 2016

PETER BUNDSCHUH  and
KEIJO VÄÄNÄNEN
PETER BUNDSCHUH*
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany email pb@math.uni-koeln.de
KEIJO VÄÄNÄNEN
Affiliation:
Department of Mathematical Sciences, University of Oulu, PO Box 3000, 90014 Oulu, Finland email keijo.vaananen@oulu.fi
*
✉pb@math.uni-koeln.de
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Abstract

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We study transcendence properties of certain infinite products of cyclotomic polynomials. In particular, we determine all cases in which the product is hypertranscendental. We then use various results from Mahler’s transcendence method to obtain algebraic independence results on such functions and their values.

Keywords

infinite productscyclotomic polynomialshypertranscendencealgebraic independenceMahler’s method

MSC classification

Primary: 11J91: Transcendence theory of other special functions
Secondary: 11J81: Transcendence (general theory) 12H05: Differential algebra 11J25: Diophantine inequalities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 375 - 387
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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