Universität zu Köln

Bridges, Walter ORCID: 0000-0002-3967-7620, Franke, Johann and Garnowski, Taylor (2022). Asymptotics for the twisted eta-product and applications to sign changes in partitions. Res. Math. Sci., 9 (4). CHAM: SPRINGER INT PUBL AG. ISSN 2197-9847

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Abstract

We prove asymptotic formulas for the complex coefficients of (zeta q; q)(infinity)(-1), where zeta is a root of unity, and apply our results to determine secondary terms in the asymptotics for p(a, b, n), the number of integer partitions of n with number of parts congruent a modulo b. Our results imply that, as n -> infinity, the difference p(a(1), b, n) - p(a(2), b, n) for a(1) not equal a(2) oscillates like a cosine when renormalized by elementary functions. Moreover, we give asymptotic formulas for arbitrary linear combinations of {p(a, b, n)}(1 <= a <= b).

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bridges, Walter UNSPECIFIED orcid.org/0000-0002-3967-7620 UNSPECIFIED Franke, Johann UNSPECIFIED UNSPECIFIED UNSPECIFIED Garnowski, Taylor UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-658486
DOI:	10.1007/s40687-022-00355-x
Journal or Publication Title:	Res. Math. Sci.
Volume:	9
Number:	4
Date:	2022
Publisher:	SPRINGER INT PUBL AG
Place of Publication:	CHAM
ISSN:	2197-9847
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/65848