English

Diophantine inequalities for generic ternary diagonal forms

Number Theory 2018-01-12 v1

Abstract

Let k\geq 2 and consider the Diophantine inequality |x_1^k-\alp_2 x_2^k-\alp_3 x_3^k| <\tet. Our goal is to find non-trivial solutions in the variables x_i, 1\leq i\leq 3, all of size about P, assuming that \tet is sufficiently large. We study this problem on average over \alp_3 and generalize previous work of Bourgain on quadratic ternary diagonal forms to general degree k.

Keywords

Cite

@article{arxiv.1801.03735,
  title  = {Diophantine inequalities for generic ternary diagonal forms},
  author = {Damaris Schindler},
  journal= {arXiv preprint arXiv:1801.03735},
  year   = {2018}
}

Comments

16 pages

R2 v1 2026-06-22T23:42:34.530Z