GAPS BETWEEN HEXAGONAL AND SQUARE LATTICES
Abstract
Abstract Let $\triangle $ denote the integers represented by the quadratic form $x^2+3y^2$ and denote the numbers represented as a sum of two squares. For a nonzero integer a , let be the set of integers n such that $n \in \triangle $ and . We conduct a census of in short intervals by showing that there exists a constant $H_{a}> 0$ with for large x . To derive this result and its generalisation, we use a theorem of Tolev [‘On the remainder term in the circle problem in an arithmetic progression’, Proc. Steklov Inst. Math. 276 (2012), 261–274].
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Bulletin of the Australian Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–15
- Publication date
- 11 May 2026
- Language
- EN