On asymptotic formulas for certain q-series involving partial theta functions

Sihun Jo; Byungchan Kim

doi:10.1090/proc/12166

On asymptotic formulas for certain q-series involving partial theta functions

Sihun Jo, Byungchan Kim

School of Natural Sciences

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

5 Scopus citations

Abstract

In this article, we investigate the integer sequence a_d(n), where for a positive integer d, a_d(n) is defined by (Fourmula Presented) In particular, we will present a combinatorial model for a_d(n) via integer partitions and this will play a crucial role in obtaining an asymptotic formula for a_d(n). Moreover, we will show that p(n) − 2a_d(n) has an unexpected sign pattern via combinatorial arguments and asymptotic formulas.

Original language	English
Pages (from-to)	3253-3263
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	8
DOIs	https://doi.org/10.1090/proc/12166
State	Published - 2015

Keywords

Asymptotic formula
Integer partitions
Partial theta function

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10.1090/proc/12166

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title = "On asymptotic formulas for certain q-series involving partial theta functions",

abstract = "In this article, we investigate the integer sequence ad(n), where for a positive integer d, ad(n) is defined by (Fourmula Presented) In particular, we will present a combinatorial model for ad(n) via integer partitions and this will play a crucial role in obtaining an asymptotic formula for ad(n). Moreover, we will show that p(n) − 2ad(n) has an unexpected sign pattern via combinatorial arguments and asymptotic formulas.",

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AU - Kim, Byungchan

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N2 - In this article, we investigate the integer sequence ad(n), where for a positive integer d, ad(n) is defined by (Fourmula Presented) In particular, we will present a combinatorial model for ad(n) via integer partitions and this will play a crucial role in obtaining an asymptotic formula for ad(n). Moreover, we will show that p(n) − 2ad(n) has an unexpected sign pattern via combinatorial arguments and asymptotic formulas.

AB - In this article, we investigate the integer sequence ad(n), where for a positive integer d, ad(n) is defined by (Fourmula Presented) In particular, we will present a combinatorial model for ad(n) via integer partitions and this will play a crucial role in obtaining an asymptotic formula for ad(n). Moreover, we will show that p(n) − 2ad(n) has an unexpected sign pattern via combinatorial arguments and asymptotic formulas.

KW - Asymptotic formula

KW - Integer partitions

KW - Partial theta function

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On asymptotic formulas for certain q-series involving partial theta functions

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Keywords

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