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arXiv · 1505.04230

On a distribution function of a probability measure involving a permutation

Yuichi Kamiya·Tatsuya Okada·Takeshi Sekiguchi·Yasunobu Shiota
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Abstract

In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums. [3,Theorem 4] states that the higher order derivatives of the distribution function with respect to a certain parameter are expressed by a generalization of the Takagi function. In [3], we only gave the sketch of the proof of Theorem 4, because the complete proof is very long. The purpose of this paper is to give the complete proof of [3,Theorem 4].

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Yuichi Kamiya, Tatsuya Okada, Takeshi Sekiguchi, Yasunobu Shiota. 2015-05-16. On a distribution function of a probability measure involving a permutation. https://arxiv.org/abs/1505.04230

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