In recent years the problem of evaluating the determinants of Laplacians on Riemannian manifolds has received considerable attention. The theory of multiple gamma functions play an important role in computations of determinants of Laplacians on manifolds of constant curvature. These functions were introduced by E. W. Barnes in about 1900. / We are particularly interested in the functional determinant for the n-sphere S$\sp{n}$ with the standard metric. For all n we give a factorization it into multiple gamma functions and use this factorization to compute nice closed form expressions for the determinant in cases n = 1, 2 and 3. / In the course of this investigation we give a new proof of the multiplication formulas for the simple and double gamma functions. / Source: Dissertation Abstracts International, Volume: 52-03, Section: B, page: 1476. / Major Professor: J. Quine. / Thesis (Ph.D.)--The Florida State University, 1991.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_78446 |
| Contributors | Choi, Junesang., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 135 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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