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.
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