On zeros of the derivative of the Selberg zeta function
Copyright policy )On zeros of the derivative of the Selberg zeta function
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.
Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Spectral theory; trace formulas (e.g., that of Selberg), Weyl formula, eigenvalues, Selberg zeta function, cocompact Fuchsian group
Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Spectral theory; trace formulas (e.g., that of Selberg), Weyl formula, eigenvalues, Selberg zeta function, cocompact Fuchsian group
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