| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
There are deep connections between the distributions of the spectra of the Laplacian and the prime geodesics of hyperbolic manifolds of finite volume derived from discrete subgroups of a semi-simple Lie group of real rank one. The aim of this study is to characterize the corresponding manifolds by studying the two distributions in relation to each other using Selberg's trace formula. During the course of this study, we evaluated the values of the Selberg zeta functions in the non-absolute convergence region for various arithmetic groups, including congruence subgroups and co-compact groups derived from indefinite quaternion algebras. We also generalized and extended the universality theorems of the Selberg zeta function from existing researches.
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