Composition-Theoretic series and false theta functions

Research output: Contribution to book or proceedingConference articlepeer-review

Abstract

Many natural partition-Theoretic series can be equally readily interpreted as composition-Theoretic series, but this viewpoint seems to have not been much employed in either theory. We consider some of the consequences of this viewpoint. As examples, we give results concerning the reciprocals of Ramanujan's theta functions and of the false theta functions of L. J. Rogers, and raise an array of questions related to these. Part of this study may be considered a natural dual of the truncated pentagonal number theorem of Andrews and Merca.

Original languageEnglish
Title of host publicationCombinatorial Number Theory - Proceedings of the Integers Conference 2023
EditorsBruce M. Landman, Florian Luca, Melvyn B. Nathanson, Jaroslav Nesetril, Aaron Robertson
PublisherWalter de Gruyter GmbH
Pages151-168
Number of pages18
ISBN (Electronic)9783111395593
DOIs
StatePublished - Oct 15 2024
EventIntegers Conference on Combinatorial Number Theory 2023 - Athens, Georgia
Duration: May 17 2023May 20 2023

Publication series

NameDe Gruyter Proceedings in Mathematics
ISSN (Print)2942-4801
ISSN (Electronic)2942-4828

Conference

ConferenceIntegers Conference on Combinatorial Number Theory 2023
Country/TerritoryGeorgia
CityAthens
Period05/17/2305/20/23

Scopus Subject Areas

  • Applied Mathematics

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