English

On Toric Orbits in the Affine Sieve

Number Theory 2022-12-26 v1

Abstract

We give a detailed analysis of a heuristic model for the failure of "saturation" in instances of the Affine Sieve having toral Zariski closure. Based on this model, we formulate precise conjectures on several classical problems of arithmetic interest, and test these against empirical data.

Cite

@article{arxiv.1808.03235,
  title  = {On Toric Orbits in the Affine Sieve},
  author = {Alex Kontorovich and Jeff Lagarias},
  journal= {arXiv preprint arXiv:1808.03235},
  year   = {2022}
}

Comments

20 pages, 6 figures

R2 v1 2026-06-23T03:29:06.924Z