Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3306
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.
Keywords
Discrete fractional integral operators, lattice points on curves, diophantine approximation
First Page
2867
Last Page
2889
Recommended Citation
TEMUR, FARUK
(2022)
"Discrete fractional integrals, lattice points on short arcs, and diophantine approximation,"
Turkish Journal of Mathematics: Vol. 46:
No.
7, Article 20.
https://doi.org/10.55730/1300-0098.3306
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss7/20
