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PreprintarXiv licencearXiv

The variance of the number of lattice points in narrow sectors

  • Stephen Lester
  • Ezra Waxman
  • Nadav Yesha
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Abstract

We study the variance of the number of lattice points in smoothed narrow sectors, where the average is taken over the position of the sectors. There are three regimes corresponding to specific ranges for the open angle of the sectors and in each we obtain an asymptotic formula for the variance.

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Cite

BibTeXRIS
BibTeX
@misc{lester2026variance,
  title = {{The variance of the number of lattice points in narrow sectors}},
  author = {Stephen Lester and Ezra Waxman and Nadav Yesha},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23214},
  eprint = {2609.23214},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23214},
}
RIS
TY  - UNPB
TI  - The variance of the number of lattice points in narrow sectors
AU  - Stephen Lester
AU  - Ezra Waxman
AU  - Nadav Yesha
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.23214
UR  - https://arxiv.org/abs/2609.23214
AB  - We study the variance of the number of lattice points in smoothed narrow sectors, where the average is taken over the position of the sectors. There are three regimes corresponding to specific ranges for the open angle of the sectors and in each we obtain an asymptotic formula for the variance.
ER  -