Spacing statistics of the Farey sequence
Speaker: Bittu
Date: Fri, Jun 21, 2024
Location: PIMS, University of British Columbia
Conference: Comparative Prime Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Fri, Jun 21, 2024
Location: PIMS, University of British Columbia
Conference: Comparative Prime Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
The Farey sequence $\mathcal{F}_Q$ of order $Q$ is the ascending sequence of fractions $\frac{a}{b}$ in the unit interval $(0, 1]$ with $gcd(a, b) = 1$ and $0 < a \leq b \leq Q$. The study of the Farey fractions is of major interest because of their role in problems related to Diophantine approximation. Also, there is a connection between the distribution of Farey fractions and the Riemann hypothesis, which further motivates their study. In this talk, we will discuss the distribution of Farey fractions with some divisibility constraints on denominators by studying their pair-correlation measure. This is based on joint work with Sneha Chaubey.
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