English

Regular ternary polygonal forms

Number Theory 2020-05-11 v4

Abstract

Inspired by Dickson's classification of regular ternary quadratic forms, we prove that there are no primitive regular mm-gonal forms when mm is sufficiently large. In order to do so, we construct sequences of primes that are inert in a certain quadratic field and show that they satisfy a certain inequality bounding the next prime by the product of the previous primes, a question of independent interest.

Keywords

Cite

@article{arxiv.1905.01423,
  title  = {Regular ternary polygonal forms},
  author = {Zilong He and Ben Kane},
  journal= {arXiv preprint arXiv:1905.01423},
  year   = {2020}
}
R2 v1 2026-06-23T08:56:50.291Z