2016 Fiscal Year Final Research Report
Research on distributions of prime geodesics and spectra of Laplacians on hyperbolic manifolds
| Project/Area Number |
26800020
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 跡公式 / セルバーグゼータ関数 / length spectrum / ラプラシアン / 不定値2元2次形式 |
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| Outline of Final Research Achievements |
It has been well-known that there are deep connections between the distributions of primitive geodesics and spectrum of the Laplacian for hyperbolic manifolds derived from discrete subgroups of semi-simple Lie group, and they are important factors to characterize manifolds (and their fundamental groups). In this research, we aim to study these distributions by using Selberg's trace formula. We proposed, in this research, estimations of the values of Selberg's zeta functions for congruence subgroups on the non- absolute convergence areas by using a limit formula derived from the prime geodesic theorem. We further obtained an asymptotic formula for class number sums of quadratic forms associated with the trace formulas for Hecke operators.
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| Free Research Field |
数物系科学
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