Jang, Min-Joo (2018). Mock theta functions and asymptotics for partition-theoretic functions. PhD thesis, Universität zu Köln.

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Abstract

This thesis contains research articles on various topics in the theory of mod- ular forms and integer partitions. First we revisit Ramanujan’s original defini- tion of a mock theta function. We solve the general problem of understanding Ramanujan’s definition explicitly for the universal mock theta function g3, an- swering a question of Rhoades. After that we study a new spt function and its crank function. We investigate asymptotic aspects of this crank function and confirm a positivity conjecture of the crank. We further analyze a sign pattern of the crank and obtain linear congruences of the spt function via its mock modularity. Finally we provide the asymptotic formula for so-called odd-even partitions whose generating function appears in Ramanujan’s identities. We also study their overpartition analogue odd-even overpartitions.

Item Type: Thesis (PhD thesis)
Creators:
CreatorsEmailORCID
Jang, Min-Joolilac3379@naver.comUNSPECIFIED
URN: urn:nbn:de:hbz:38-81830
Subjects: Mathematics
Uncontrolled Keywords:
KeywordsLanguage
Mock theta functionsEnglish
AsymptoticsEnglish
partitionsEnglish
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Language: English
Date: 8 April 2018
Date of oral exam: 8 March 2018
Referee:
NameAcademic Title
Bringmann, KathrinProf. Dr.
Zwegers, SanderProf. Dr.
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/8183

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