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On infinite products of functions in compact riemann surfaces

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Abstract

Letν′ be the complementary of a point ∞ in a compact Riemann surfaceν. The normal convergence in compact subsets ofν′ of an infinite product of meromorphic functions (with polynomic exponential singularities at ∞ of bounded degree) is shown in this paper to be equivalent to a certain type of convergence of the double series of Newton sums of the divisors of its factors. This applies, for instance, to products of Baker functions inν′ and to products of meromorphic functions inν. The result for this last case is also generalized to complementaries of arbitrary nonvoid finite subsets ofν.

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Authors and Affiliations

  1. Dpto. Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008, Salamanca, Spain

    Pascual Cutillas Ripoll

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  1. Pascual Cutillas Ripoll
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Research supported by SA30/00B.

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Ripoll, P.C. On infinite products of functions in compact riemann surfaces. Isr. J. Math. 152, 349–370 (2006). https://doi.org/10.1007/BF02771991

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  • DOI: https://doi.org/10.1007/BF02771991

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