On spt-crank-type functions

Min Joo Jang; Byungchan Kim

doi:10.1007/s11139-016-9838-5

On spt-crank-type functions

Min Joo Jang, Byungchan Kim

School of Natural Sciences

University of Cologne

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

3 Scopus citations

Abstract

In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function spt _ω(n) , which is closely related to Ramanujan’s third-order mock theta function ω(q). Garvan and Jennings-Shaffer introduced a crank function which explains congruences for spt _ω(n). In this article, we study the asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We also study a sign pattern of the crank and congruences for spt _ω(n).

Original language	English
Pages (from-to)	211-225
Number of pages	15
Journal	Ramanujan Journal
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s11139-016-9838-5
State	Published - 1 Jan 2018

Keywords

Asymptotic formula
Congruences
Partial theta function
Spt function
Spt-crank function

Access to Document

10.1007/s11139-016-9838-5

Cite this

@article{30b916a73b8442428cf90b23d663c3df,

title = "On spt-crank-type functions",

abstract = "In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function spt ω(n) , which is closely related to Ramanujan{\textquoteright}s third-order mock theta function ω(q). Garvan and Jennings-Shaffer introduced a crank function which explains congruences for spt ω(n). In this article, we study the asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We also study a sign pattern of the crank and congruences for spt ω(n).",

keywords = "Asymptotic formula, Congruences, Partial theta function, Spt function, Spt-crank function",

author = "Jang, \{Min Joo\} and Byungchan Kim",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/s11139-016-9838-5",

language = "English",

volume = "45",

pages = "211--225",

journal = "Ramanujan Journal",

issn = "1382-4090",

number = "1",

}

TY - JOUR

T1 - On spt-crank-type functions

AU - Jang, Min Joo

AU - Kim, Byungchan

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function spt ω(n) , which is closely related to Ramanujan’s third-order mock theta function ω(q). Garvan and Jennings-Shaffer introduced a crank function which explains congruences for spt ω(n). In this article, we study the asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We also study a sign pattern of the crank and congruences for spt ω(n).

AB - In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function spt ω(n) , which is closely related to Ramanujan’s third-order mock theta function ω(q). Garvan and Jennings-Shaffer introduced a crank function which explains congruences for spt ω(n). In this article, we study the asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We also study a sign pattern of the crank and congruences for spt ω(n).

KW - Asymptotic formula

KW - Congruences

KW - Partial theta function

KW - Spt function

KW - Spt-crank function

UR - http://www.scopus.com/inward/record.url?scp=84994107406&partnerID=8YFLogxK

U2 - 10.1007/s11139-016-9838-5

DO - 10.1007/s11139-016-9838-5

M3 - Article

AN - SCOPUS:84994107406

SN - 1382-4090

VL - 45

SP - 211

EP - 225

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1

ER -

On spt-crank-type functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this