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- W2963552695 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{GI1}, cite{GI2} 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." @default.
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- W2963552695 date "2007-01-01" @default.
- W2963552695 modified "2023-09-26" @default.
- W2963552695 title "Variation of argument and Bernstein index for holomorphic functions on Riemann surfaces" @default.
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- W2963552695 doi "https://doi.org/10.4310/mrl.2007.v14.n3.a8" @default.
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