Congruences related to an eighth order mock theta function of Gordon and McIntosh

Eduardo H.M. Brietzke; Robson da Silva; James A. Sellers

doi:10.1016/j.jmaa.2019.06.016

Congruences related to an eighth order mock theta function of Gordon and McIntosh

Eduardo H.M. Brietzke, Robson da Silva, James A. Sellers

Mathematics & Statistics

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

12 Scopus citations

Abstract

In this paper, we study arithmetic properties of a partition function related to an eighth order mock theta function of Gordon and McIntosh. Via elementary generating function manipulations, a complete characterization of the parity of this function is presented, from which infinitely many Ramanujan-like congruences modulo 2 are obtained. In addition, many congruences modulo certain numbers of the form 2^α3^β5 are presented.

Original language	English (US)
Pages (from-to)	62-89
Number of pages	28
Journal	Journal of Mathematical Analysis and Applications
Volume	479
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2019.06.016
State	Published - Nov 1 2019

Bibliographical note

Funding Information:
The second author was supported by FAPESP (grant no. 2016/14057-2 ).

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Congruences
Mock theta function
Partition

Publisher link

10.1016/j.jmaa.2019.06.016

Find It

Find It at U of M Libraries

Cite this

@article{ae48b3cde291492880d9ae526946a31d,

title = "Congruences related to an eighth order mock theta function of Gordon and McIntosh",

abstract = "In this paper, we study arithmetic properties of a partition function related to an eighth order mock theta function of Gordon and McIntosh. Via elementary generating function manipulations, a complete characterization of the parity of this function is presented, from which infinitely many Ramanujan-like congruences modulo 2 are obtained. In addition, many congruences modulo certain numbers of the form 2α3β5 are presented.",

keywords = "Congruences, Mock theta function, Partition",

author = "Brietzke, {Eduardo H.M.} and {da Silva}, Robson and Sellers, {James A.}",

note = "Funding Information: The second author was supported by FAPESP (grant no. 2016/14057-2 ). Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = nov,

day = "1",

doi = "10.1016/j.jmaa.2019.06.016",

language = "English (US)",

volume = "479",

pages = "62--89",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Congruences related to an eighth order mock theta function of Gordon and McIntosh

AU - Brietzke, Eduardo H.M.

AU - da Silva, Robson

AU - Sellers, James A.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In this paper, we study arithmetic properties of a partition function related to an eighth order mock theta function of Gordon and McIntosh. Via elementary generating function manipulations, a complete characterization of the parity of this function is presented, from which infinitely many Ramanujan-like congruences modulo 2 are obtained. In addition, many congruences modulo certain numbers of the form 2α3β5 are presented.

AB - In this paper, we study arithmetic properties of a partition function related to an eighth order mock theta function of Gordon and McIntosh. Via elementary generating function manipulations, a complete characterization of the parity of this function is presented, from which infinitely many Ramanujan-like congruences modulo 2 are obtained. In addition, many congruences modulo certain numbers of the form 2α3β5 are presented.

KW - Congruences

KW - Mock theta function

KW - Partition

UR - http://www.scopus.com/inward/record.url?scp=85067179083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067179083&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2019.06.016

DO - 10.1016/j.jmaa.2019.06.016

M3 - Article

AN - SCOPUS:85067179083

SN - 0022-247X

VL - 479

SP - 62

EP - 89

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Congruences related to an eighth order mock theta function of Gordon and McIntosh

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this