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INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS

Part of: Series expansions Algebraic number theory: global fields Sequences and sets Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  26 February 2015

WILLIAM DUKE  and
HA NAM NGUYEN
WILLIAM DUKE*
Affiliation:
Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, CA 90095-1555, USA email [email protected]
HA NAM NGUYEN
Affiliation:
Department of Mathematics, California State University, 18111 Nordhoff Street, Northridge, CA 91330, USA email [email protected]
*
✉[email protected]
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Abstract

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We study analytic properties of certain infinite products of cyclotomic polynomials that generalise some products introduced by Mahler. We characterise those that have the unit circle as a natural boundary and use associated Dirichlet series to obtain their asymptotic behaviour near roots of unity.

Keywords

infinite productscyclotomic polynomialsnatural boundaryMahler functionsStern diatomic sequence

MSC classification

Primary: 11M41: Other Dirichlet series and zeta functions
Secondary: 11B85: Automata sequences 11R18: Cyclotomic extensions 30B30: Boundary behavior of power series, over-convergence
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 3 , June 2015 , pp. 400 - 411
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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