Variation of argument and Bernstein index for holomorphic functions on Riemann surfaces
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Publication:2459329
DOI10.4310/MRL.2007.V14.N3.A8zbMATH Open1138.30025arXivmath/0601043OpenAlexW2963552695MaRDI QIDQ2459329
Publication date: 6 November 2007
Published in: Mathematical Research Letters (Search for Journal in Brave)
Abstract: An upper bound of the variation of argument of a holomorphic function along a curve on a Riemann surface is given. This bound is expressed through the Bernstein index of the function multiplied by a geometric constant. The Bernstein index characterizes growth of the function from a smaller domain to a larger one. The geometric constant in the estimate is explicitly given. This result is applied in cite {GI} to the solution of the restricted version of the infinitesimal Hilbert 16th problem, namely, to upper estimates of the number of zeros of abelian integrals in complex domains.
Full work available at URL: https://arxiv.org/abs/math/0601043
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