Chebyshev's bias for irrational factor function

2025/05/05 by Bittu Chahal, Chahal, Bittu · 1 citation
Engineering · Mathematics · #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.02968

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the distribution of the irrational factor function of order k, introduced first by Atanassov for k=2 and later it was generalized by Dong et al. for all k≥ 2. We introduce the irrational factor function in both number field and function field settings, derive asymptotic formulas for their average value, and further establish omega results for the error term in the asymptotic formulas. Moreover, we study the Chebyshev's bias phenomenon for number field and function field analogues of sum of the irrational factor function.

Citations

• On the distribution of index of Farey Sequences
• Prime Number Races
• Sur la distribution des nombres premiers

Cited by

• Distribution of Farey fractions with k-free denominators

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