Discrete fractional integrals, lattice points on short arcs, and diophantine approximation

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 establishin...

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Bibliographic Details
Published inarXiv.org
Main Author Temur, Faruk
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.12.2020
Subjects
Approximation
Bivariate analysis
Conics
Integrals
Mathematical analysis
Operators (mathematics)
Polynomials
Quadratic forms
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ISSN2331-8422

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Summary: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.
Bibliography:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422