Bringmann, Kathrin ORCID: 0000-0001-7126-1409, Dousse, Jehanne, Lovejoy, Jeremy and Mahlburg, Karl (2015). Overpartitions with restricted odd differences. Electron. J. Comb., 22 (3). NEWARK: ELECTRONIC JOURNAL OF COMBINATORICS. ISSN 1077-8926

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Abstract

We use q-difference equations to compute a two-variable q-hypergeometric generating function for overpartitions where the difference between two successive parts may be odd only if the larger part is overlined. This generating function specializes in one case to a modular form, and in another to a mixed mock modular form. We also establish a two-variable generating function for the same overpartitions with odd smallest part, and again find modular and mixed mock modular specializations. Applications include linear congruences arising from eigenforms for 3-adic Hecke operators, as well as asymptotic formulas for the enumeration functions. The latter are proven using Wright's variation of the circle method.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Bringmann, KathrinUNSPECIFIEDorcid.org/0000-0001-7126-1409UNSPECIFIED
Dousse, JehanneUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Lovejoy, JeremyUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Mahlburg, KarlUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-398587
Journal or Publication Title: Electron. J. Comb.
Volume: 22
Number: 3
Date: 2015
Publisher: ELECTRONIC JOURNAL OF COMBINATORICS
Place of Publication: NEWARK
ISSN: 1077-8926
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
MOCK THETA-FUNCTIONS; FOURIER COEFFICIENTS; FORMSMultiple languages
Mathematics, Applied; MathematicsMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/39858

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