Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker’s first limit formula
| dc.contributor.author | McIntyre, Andrew | |
| dc.contributor.author | Takhtajan, Leon A. | |
| dc.date.accessioned | 2016-12-09T18:59:21Z | |
| dc.date.available | 2016-12-09T18:59:21Z | |
| dc.date.issued | 2006-09 | |
| dc.description.abstract | For a family of compact Riemann surfaces X_t of genus g>1 parametrized by the Schottky space S_g, we define a natural basis for the holomorphic n-differentials on X_t which varies holomorphically with t and generalizes the basis of normalized abelian differentials of the first kind for n=1. We introduce a holomorphic function F(n) on S_g which generalizes the classical product \prod(1-q^m)^2 appearing in the Dedekind eta function for n=1 and g=1. We prove a holomorphic factorization formula expressing the regularized determinant of the Laplacian as a product of |F(n)|^2, a holomorphic anomaly depending on the classical Liouville action (a Kahler potential of S_g), and the determinant of the Gram matrix of the natural basis. The factorization formula reduces to Kronecker's first limit formula when n=1 and g=1, and to Zograf's factorization formula for n=1 and g>1. | en_US |
| dc.identifier.citation | McIntyre, A. & Takhtajan, L.A. GAFA, Geom. funct. anal. (2006) 16: 1291. doi:10.1007/s00039-006-0582-7 | en_US |
| dc.identifier.uri | http://hdl.handle.net/11209/10687 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer Verlag | en_US |
| dc.subject | Schottky group | en_US |
| dc.subject | determinant of Laplacian | en_US |
| dc.subject | Kronecker limit formula | en_US |
| dc.subject | Dedekind eta function | en_US |
| dc.subject | Liouville action | en_US |
| dc.subject | Schottky space | en_US |
| dc.subject | Teichmüller space | en_US |
| dc.subject | Green’s function | en_US |
| dc.title | Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker’s first limit formula | en_US |
| dc.type | Article | en_US |
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