Rational numbers with small denominators in short intervals

2023/11/28 by Igor E. Shparlinski, Shparlinski, Igor E. · 1 citation
Computer Science · Mathematics · #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.16640

openalex publication_date 2023/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use bounds on bilinear forms with Kloosterman fractions and improve the error term in the asymptotic formula of Balazard and Martin (2023) on the average value of the smallest denominators of rational numbers in short intervals.

Cited by

• Minimal Denominators Lying in Subsets of the Ring of Polynomials over a Finite Field

Related

• On Unit Fractions with Denominators in Short Intervals
• Lowest Terms Revisited
• Démonstration d'une conjecture de Kruyswijk et Meijer sur le plus petit dénominateur des nombres rationnels d'un intervalle
• Smallest denominators
• A note on Farey fractions with denominators in arithmetic progressions