English

On a distribution function of a probability measure involving a permutation

Number Theory 2015-05-19 v1

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].

Keywords

Cite

@article{arxiv.1505.04230,
  title  = {On a distribution function of a probability measure involving a permutation},
  author = {Yuichi Kamiya and Tatsuya Okada and Takeshi Sekiguchi and Yasunobu Shiota},
  journal= {arXiv preprint arXiv:1505.04230},
  year   = {2015}
}
R2 v1 2026-06-22T09:35:20.665Z