Distribuion of Leading Digits of Numbers II

Uniform distribution theory Pub Date : 2019-06-01 DOI:10.2478/udt-2019-0003

Y. Ohkubo, O. Strauch

引用次数: 2

Abstract

Abstract In this paper, we study the sequence (f (pn))n≥1,where pn is the nth prime number and f is a function of a class of slowly increasing functions including f (x)=logb xr and f (x)=logb(x log x)r,where b ≥ 2 is an integer and r> 0 is a real number. We give upper bounds of the discrepancy DNi*(f(pn),g) D_{{N_i}}^*\left( {f\left( {{p_n}} \right),g} \right) for a distribution function g and a sub-sequence (Ni)i≥1 of the natural numbers. Especially for f (x)= logb xr, we obtain the effective results for an upper bound of D Ni*(f(pn)g) D_{{N_i}}^*\left( {f\left( {{p_n}} \right),g} \right) .

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数前导数的分布2

摘要本文研究了序列(f (pn))n≥1，其中pn为第n个素数，f为f (x)=logb(x log x)r和f (x)=logb(x log x)r这类缓增函数的函数，其中b≥2为整数，r> 0为实数。对于一个分布函数g和一个自然数的子序列(Ni)i≥1，我们给出了差异DNi*(f(pn)，g) D_{{N_i}}^*\left({f\left({{p_n}} \right)，g} \right)的上界。特别是对于f(x)= logbxr，我们得到了D Ni*(f(pn)g) D_{{N_i}}^*\左({f\左({{p_n}} \右)，g} \右)上界的有效结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Uniform distribution theory

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