Note on zeros of the derivative of the Selberg zeta-function
Wenzhi Luo studied the distribution of nontrivial zeros of the derivatives of Selberg zeta-functions on cocompact hyperbolic surfaces, and obtained an asymptotic formula for zero density with bounded height. Then he related the distribution of zeros to the multiplicities of Laplacian eigenvalues. Using better bounds for the growth of the Selberg zeta-functions we improve some of the above results.
Keywords.Selberg zeta-function zero distribution Lindelöf hypothesis
Mathematics Subject Classification (2000).Primary 11M36 Secondary 30F35
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