English

A Finitary Hasse Principle for Diagonal Curves

Number Theory 2014-04-11 v1

Abstract

We prove a Hasse principle for solving equations of the form ax+by+cz=0 where x, y, z belong to a given finite index subgroup of the multiplicative group of rational numbers. From this we deduce a Hasse principle for diagonal curves over fields of algebraic numbers with finitely generated Galois group.

Keywords

Cite

@article{arxiv.1404.2849,
  title  = {A Finitary Hasse Principle for Diagonal Curves},
  author = {Jean Bourgain and Michael Larsen},
  journal= {arXiv preprint arXiv:1404.2849},
  year   = {2014}
}

Comments

11 pages

R2 v1 2026-06-22T03:48:03.621Z