%0 Journal Article
%T An inequality for the zeta function of a planar domain
%A Alexandre Jollivet
%A Vladimir Sharafutdinov
%J Physics
%D 2015
%I arXiv
%X We consider the zeta function $\zeta\_\Omega$ for the Dirichlet-to-Neumann operator of a simply connected planar domain $\Omega$ bounded by a smooth closed curve.We prove non-negativeness and growth properties for $\zeta\_\Omega(s)-2\big({L(\partial \Omega)\over 2\pi}\big)^s\zeta\_R(s)\ (s\leq-1)$, where $L(\partial \Omega)$ is the length of the boundary curve and $\zeta\_R$ stands for the classical Riemann zeta function.Two analogs of these results are also provided.
%U http://arxiv.org/abs/1510.06548v1