Rational numbers with small denominators in short intervals

DOI10.1007/s00013-024-01993-zMaRDI QIDQ6536631

Igor E. Shparlinski

Publication date: 13 May 2024

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

Farey fractionsshort intervalsKloosterman fractions

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Farey sequences; the sequences (1^k, 2^k, dots) (11B57)

Cites Work

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• Bilinear forms with Kloosterman fractions
• Trilinear forms with Kloosterman fractions
• Translates of rational points along expanding closed horocycles on the modular surface
• On the Distribution of Small Denominators in the Farey Series of Order N
• Fine-Scale Statistics for the Multidimensional Farey Sequence
• Some extremal functions in Fourier analysis
• Expected value of the smallest denominator in a random interval of fixed radius
• Proof of a conjecture of Kruyswijk and Meijer on the smallest denominator of rational numbers of an interval
• Smallest denominators

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