Abstract
In this paper for a slowly increasing exponential function we study the degree of deviation of the distribution of the sequence of its fractional parts from the “ideal” uniform distribution. An estimate is given which can appropriately be called the measure of irregularity of the distribution of a given sequence.
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References
E. Titchmarsh,The Theory of the Riemann Zeta-Function, Oxford (1951).
A. A. Karatsuba,Foundations of the Analytic Theory of Numbers [in Russian], Nauka, Moscow (1983).
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Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 148–152, January, 1999.
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Usol’tsev, L.P. On the distribution of the sequence of fractional parts of a slowly increasing exponential function. Math Notes 65, 124–127 (1999). https://doi.org/10.1007/BF02675017
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DOI: https://doi.org/10.1007/BF02675017