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Title: Discrete fractional integrals, lattice points on short arcs, and diophantine approximation
Authors: Temur, Faruk
Keywords: Diophantine approximation
Lattice points on curves
Discrete fractional integral operators
Issue Date: 2022
Publisher: TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu
Abstract: Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate quadratic polynomials. We achieve this in part by establishing connections to problems on concentration of lattice points on short arcs of conics, whence we study discrete fractional integrals and lattice point concentration from a unified perspective via tools of sieving and diophantine approximation, and prove theorems that are of interest to researchers in both subjects.
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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