Asymptotics for q-expansions involving partial theta functions

Byungchan Kim; Eunmi Kim; Jeehyeon Seo

doi:10.1016/j.disc.2014.09.011

Asymptotics for q-expansions involving partial theta functions

Byungchan Kim
, Eunmi Kim
, Jeehyeon Seo

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We obtain effective asymptotics for the coefficients of q-expansions which involve partial theta functions. As applications, we obtain effective asymptotics for ranks, and cranks of integer partitions. Moreover, from these effective estimates, we obtain asymptotic inequalities among them with effective lower bounds.

Original language	English
Pages (from-to)	180-189
Number of pages	10
Journal	Discrete Mathematics
Volume	338
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2014.09.011
State	Published - 6 Feb 2015

Keywords

Asymptotics
Crank
Effective bound
Partial theta function
Partitions
Rank

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10.1016/j.disc.2014.09.011

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title = "Asymptotics for q-expansions involving partial theta functions",

abstract = "We obtain effective asymptotics for the coefficients of q-expansions which involve partial theta functions. As applications, we obtain effective asymptotics for ranks, and cranks of integer partitions. Moreover, from these effective estimates, we obtain asymptotic inequalities among them with effective lower bounds.",

keywords = "Asymptotics, Crank, Effective bound, Partial theta function, Partitions, Rank",

author = "Byungchan Kim and Eunmi Kim and Jeehyeon Seo",

year = "2015",

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doi = "10.1016/j.disc.2014.09.011",

language = "English",

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journal = "Discrete Mathematics",

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T1 - Asymptotics for q-expansions involving partial theta functions

AU - Kim, Byungchan

AU - Kim, Eunmi

AU - Seo, Jeehyeon

PY - 2015/2/6

Y1 - 2015/2/6

N2 - We obtain effective asymptotics for the coefficients of q-expansions which involve partial theta functions. As applications, we obtain effective asymptotics for ranks, and cranks of integer partitions. Moreover, from these effective estimates, we obtain asymptotic inequalities among them with effective lower bounds.

AB - We obtain effective asymptotics for the coefficients of q-expansions which involve partial theta functions. As applications, we obtain effective asymptotics for ranks, and cranks of integer partitions. Moreover, from these effective estimates, we obtain asymptotic inequalities among them with effective lower bounds.

KW - Asymptotics

KW - Crank

KW - Effective bound

KW - Partial theta function

KW - Partitions

KW - Rank

UR - https://www.scopus.com/pages/publications/84908409012

U2 - 10.1016/j.disc.2014.09.011

DO - 10.1016/j.disc.2014.09.011

M3 - Article

AN - SCOPUS:84908409012

SN - 0012-365X

VL - 338

SP - 180

EP - 189

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -

Asymptotics for q-expansions involving partial theta functions

Abstract

Keywords

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