Term of Award
Spring 2016
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Andrew Sills
Committee Member 1
Alex Stokolos
Committee Member 2
Yi Hu
Abstract
Nearly a century ago, the mathematicians Hardy and Ramanujan established their celebrated circle method to give a remarkable asymptotic expression for the unrestricted partition function. Following later improvements by Rademacher, the method was utilized by Niven, Lehner, Iseki, and others to develop rapidly convergent series representations of various restricted partition functions. Following in this tradition, we use the circle method to develop formulas for counting the restricted classes of partitions that arise in the Gollnitz-Gordon identities. We then show that our results are strongly supported by numerical tests. As a side note, we also derive and compare the asymptotic behavior of our formulas.
Recommended Citation
Smoot, Nicolas A., "A Partition Function Connected with the Göllnitz-Gordon Identities" (2016). Electronic Theses and Dissertations. 1389.
https://digitalcommons.georgiasouthern.edu/etd/1389
