Universität zu Köln

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:	Creators Email ORCID ORCID Put Code Jang, Min-Joo lilac3379@naver.com UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-81830
Date:	8 April 2018
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:	Mathematics
Uncontrolled Keywords:	Keywords Language Mock theta functions English Asymptotics English partitions English
Date of oral exam:	8 March 2018
Referee:	Name Academic Title Bringmann, Kathrin Prof. Dr. Zwegers, Sander Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/8183