Dissertation
A polynomial version of Meinardus' theorem
Doctor of Philosophy (Ph.D.), Drexel University
May 2014
DOI:
https://doi.org/10.17918/etd-4563
Abstract
This dissertation develops and formalizes a polynomial variation of Meinardus' Theorem which is used to approximate a large class of polynomials generated by certain generating functions P(z; q) when z 2 D: Following the outline of the original Meinardus' Theorem, we begin by de ning assumptions by which we can approximate ln P(z; q) using the analytic properties of the Cahen-Mellin integral. We then apply a variant of the circle method which exploits the use of Farey series to prove our main results. The second part of the dissertation focuses on examples to which our theorem can be applied. We detail some examples of polynomial families to which can be approximated by our main theorem both of which are related to asymptotic enumeration of integer partitions.
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Details
- Title
- A polynomial version of Meinardus' theorem
- Creators
- Daniel Parry - DU
- Contributors
- Robert Paul Boyer (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 4563; 991014632594004721