English

Arithmetic progressions in binary quadratic forms and norm forms

Number Theory 2019-08-14 v2

Abstract

We prove an upper bound for the length of an arithmetic progression represented by an irreducible integral binary quadratic form or a norm form, which depends only on the form and the progression's common difference. For quadratic forms, this improves significantly upon an earlier result of Dey and Thangadurai.

Keywords

Cite

@article{arxiv.1810.11251,
  title  = {Arithmetic progressions in binary quadratic forms and norm forms},
  author = {Christian Elsholtz and Christopher Frei},
  journal= {arXiv preprint arXiv:1810.11251},
  year   = {2019}
}

Comments

7 pages; minor revision; to appear in BLMS