English

A generic effective Oppenheim theorem for systems of forms

Number Theory 2020-07-22 v2 Dynamical Systems

Abstract

We prove a uniform effective density theorem as well as an effective counting result for a generic system comprising a polynomial with a mild homogeneous condition and several linear forms using Roger's second moment formula for the Siegel transform on the space of unimodular lattices.

Keywords

Cite

@article{arxiv.2003.06114,
  title  = {A generic effective Oppenheim theorem for systems of forms},
  author = {Prasuna Bandi and Anish Ghosh and Jiyoung Han},
  journal= {arXiv preprint arXiv:2003.06114},
  year   = {2020}
}

Comments

18 pages

R2 v1 2026-06-23T14:13:34.924Z