The purpose of this dissertation is to, first outline a theory of Zeta regularized products which will work for sequences of complex numbers, and second to use this theory to compute Zeta regularized products and modular constants for sequences which are integer combinations of a fixed set of complex numbers. / The gamma function $\Gamma(z)$ is represented as the ratio of two Zeta regularized products. This relation is then extended to define multiple gamma functions as the ratio of two corresponding Zeta regularized products. A full account of the functional equations associated with multiple gamma functions is also given. The double gamma function is investigated in detail. / Some other special functions are also discussed. Namely Jacobi's theta function $\theta\sb1$, the Weierstrass sigma function $\sigma(z),$ and $P(z\vert\tau)$ defined by / The determinant of the Laplacian on an n-dimensional flat Torus is computed for $n \geq$ 2, by computing / Source: Dissertation Abstracts International, Volume: 53-07, Section: B, page: 3523. / Major Professor: John R. Quine. / Thesis (Ph.D.)--The Florida State University, 1992.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_76704 |
| Contributors | Heydari, Shahryar., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 123 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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