Joint universality theorem of Selberg zeta functions for principal congruence subgroups
Copyright policy )Joint universality theorem of Selberg zeta functions for principal congruence subgroups
Let \(Z_j(s)\) \((j=1,\ldots,r)\) be the Selberg zeta function of the principal congruence subgroup of \(\mathrm{PSL}(2,\mathbb Z)\) of level \(N_j\). Assume that \(N_j\) are coprime. Let \(K_j\) be a compact subset of the strip \(\frac{\alpha+1}20 \quad(\text{ for all } \varepsilon>0), \] where \(\nu_T(\cdots)=\frac1T\mu\{\tau\in[0,T]:\cdots\}\) with \(\mu\) the Lebesgue measure on \(\mathbb R\). This is a generalization of the theorem of [\textit{P. Drungilas} et al., Forum Math. 25, No. 3, 533--564 (2013; Zbl 1328.11093)], where they proved the case of \(r=1\) and \(N_1=1\).
- Tokyo Denki University Japan
Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), prime geodesic theorem, congruence subgroups, Selberg zeta functions, value distribution
Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), prime geodesic theorem, congruence subgroups, Selberg zeta functions, value distribution
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