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Full-Text Articles in Number Theory
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Electronic Theses and Dissertations
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …
A Partition Function Connected With The Göllnitz-Gordon Identities, Nicolas A. Smoot
A Partition Function Connected With The Göllnitz-Gordon Identities, Nicolas A. Smoot
Electronic Theses and Dissertations
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 …