On some polynomials and series of Bloch-Pólya type
Authors:
Alexander Berkovich and Ali Kemal Uncu
Journal:
Proc. Amer. Math. Soc. 146 (2018), 2827-2838
MSC (2010):
Primary 05A17, 11B65; Secondary 05A19, 05A30, 11P81
DOI:
https://doi.org/10.1090/proc/13982
Published electronically:
March 9, 2018
MathSciNet review:
3787346
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We will show that is a polynomial in
with coefficients from
iff
or 5 and explore some interesting consequences of this result. We find explicit formulas for the
-series coefficients of
and
. In doing so, we extend certain observations made by Sudler in 1964. We also discuss the classification of the products
and some related series with respect to their absolute largest coefficients.
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Additional Information
Alexander Berkovich
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611
Email:
alexb@ufl.edu
Ali Kemal Uncu
Affiliation:
Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Straße 69, A-4040 Linz, Austria
Email:
akuncu@risc.jku.at
DOI:
https://doi.org/10.1090/proc/13982
Keywords:
Pentagonal numbers,
Bloch--P\'olya type series,
$q$-series identities,
$q$-binomial theorem,
partition theorems
Received by editor(s):
June 9, 2017
Received by editor(s) in revised form:
October 9, 2017
Published electronically:
March 9, 2018
Additional Notes:
Research of the first author was partly supported by the Simons Foundation, award ID: 308929.
Research of the second author was supported by the Austrian Science Fund (FWF): SFB F50-07.
Communicated by:
Ken Ono
Article copyright:
© Copyright 2018
American Mathematical Society