On the pits effect of Littlewood and Offord - Mathematics > Complex VariablesReport as inadecuate




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Abstract: Suppose that the moduli of the coefficients of a power series are 1-n!, whilethe arguments are arbitrary. If an entire function f represented by such powerseries decreases exponentially on some ray, then it has to be an exponential.If the arguments of the coefficients are of the form 2pi n^2a, where a isirrational, then the function displays the so-called -pits effect-. Moreprecisely, under this condition, f is of completely regular growth withconstant indicator.



Author: Alexandre Eremenko, Iossif Ostrovskii

Source: https://arxiv.org/



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