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On zeros of the derivative of the Selberg zeta function
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 127, Number 5, October 2005
- pp. 1141-1151
- 10.1353/ajm.2005.0032
- Article
- Additional Information
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Abstract
In this work, we study the distribution of nontrivial zeros of the derivatives of Selberg zeta functions on cocompact hyperbolic surfaces, and obtain an asymptotic formula for the zero density with bounded height, which is an analogue of the Weyl law. We then relate the distribution of the zeros to the multiplicities of Laplacian eigenvalues.
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