On the distribution of index of Farey Sequences
Number Theory
2022-03-31 v1
Abstract
In this article, we study the distribution of index of Farey fractions which was first introduced and studied by Hall and Shiu. We provide asymptotic formulas for moments of index of Farey fractions twisted by Dirichlet characters for Farey fractions with -free denominators. Additionally, we reconsider the squarefree case earlier done in [ALVZ08], and obtain new results for moments of indices with square-free denominators. We also study higher level correlations of the index function generalizing earlier known results on two level correlations.
Keywords
Cite
@article{arxiv.2203.16215,
title = {On the distribution of index of Farey Sequences},
author = {Bittu and Sneha Chaubey and Shivani Goel},
journal= {arXiv preprint arXiv:2203.16215},
year = {2022}
}
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32 pages