An inequality for the zeta function of a planar domain

2015/10/22 by Jollivet, Alexandre, Sharafutdinov, Vladimir
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1510.06548

Abstract

We consider the zeta function ζ_Ω for the Dirichlet-to-Neumann operator of a simply connected planar domain Ω bounded by a smooth closed curve.We prove non-negativeness and growth properties for ζ_Ω(s)-2(L(∂ Ω)\over 2π)^sζ_R(s) (s≤-1), where L(∂ Ω) is the length of the boundary curve and ζ_R stands for the classical Riemann zeta function.Two analogs of these results are also provided.

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