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The Riemann ζ function and asymptotics for Stieltjes fractions

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Abstract

We study the asymptotic behaviour of the coefficients in the continued fractions corresponding to Stieltjes transforms of weight functions on a finite interval. It is shown that, in general, the coefficients with odd and even index converge to a different limit. For a specific class of weights a detailed asymptotic expansion of the coefficients is obtained. Some examples serve as illustration and an application to continued fraction expansions for the Riemann ζ function is given.

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Authors and Affiliations

  1. Universiteit Antwerpen, Antwerp, Belgium

    Joris Van Deun

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  1. Joris Van Deun
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Correspondence to Joris Van Deun.

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The author is a Postdoctoral Fellow of the Research Foundation—Flanders (FWO).

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Van Deun, J. The Riemann ζ function and asymptotics for Stieltjes fractions. Ramanujan J 21, 1–16 (2010). https://doi.org/10.1007/s11139-009-9168-y

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  • DOI: https://doi.org/10.1007/s11139-009-9168-y

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