PreprintCC BY-NC-ND 4.0arXiv
Lattice points close to a smooth curve and squarefull numbers in short intervals. II
Abstract
By applying recent estimates on the number of integer solutions of ternary quadratic forms in boxes due to Browning and Heath-Brown, we obtain new estimates for the number of lattice points close to a curve. This leads to a new result on the distribution of squarefull numbers in short intervals.
Related
- Unimodular defect and antipodal lattice points of smooth reflexive polytopes
- Schreier Sets of Intervals, Super-Schreier Sets, and Catalan Numbers
- Sharp local estimates for smooth numbers
- Suslin's cancellation conjecture on smooth real affine varieties with few real points
- Prime points on smooth hypersurfaces
BibTeX
@misc{trifonov2026lattice,
title = {{Lattice points close to a smooth curve and squarefull numbers in short intervals. II}},
author = {Ognian Trifonov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17715},
eprint = {2609.17715},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17715},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Lattice points close to a smooth curve and squarefull numbers in short intervals. II
AU - Ognian Trifonov
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17715
UR - https://arxiv.org/abs/2609.17715
AB - By applying recent estimates on the number of integer solutions of ternary quadratic forms in boxes due to Browning and Heath-Brown, we obtain new estimates for the number of lattice points close to a curve. This leads to a new result on the distribution of squarefull numbers in short intervals.
ER -