On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions
نویسندگان
چکیده
منابع مشابه
On the Growth of Logarithmic Differences, Difference Quotients and Logarithmic Derivatives of Meromorphic Functions
Abstract. We obtain growth comparison results of logarithmic differences, difference quotients and logarithmic derivatives for finite order meromorphic functions. Our results are both generalizations and extensions of previous results. We construct examples showing that the results obtained are best possible in certain sense. Our findings show that there are marked differences between the growt...
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Abstract. A crucial ingredient in the recent discovery by Ablowitz, Halburd, Herbst and Korhonen [2], [15] that a connection exists between discrete Painlevé equations and (finite order) Nevanlinna theory is an estimate of the integrated average of log |f(z + 1)/f(z)| on |z| = r. We obtained essentially the same estimate in our previous paper [8] independent of Halburd et al [14]. We continue o...
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We establish Connes’s local trace formula (related to the explicit formulae of number theory) for the quaternions. This is done as an application of a study of the central operator H = log(|x|) + log(|y|) in the context of invariant harmonic analysis. The multiplicative analysis of the additive Fourier transform gives a spectral interpretation to generalized “Tate Gamma functions” (closely akin...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2009
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-09-04663-7