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ARITHMETIC PROPERTIES OF INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS

Published online by Cambridge University Press:  08 January 2016

PETER BUNDSCHUH*
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany email [email protected]
KEIJO VÄÄNÄNEN
Affiliation:
Department of Mathematical Sciences, University of Oulu, PO Box 3000, 90014 Oulu, Finland email [email protected]
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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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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