A Finitary Hasse Principle for Diagonal Curves

2014/04/10 by Jean Bourgain, Michael Larsen, Bourgain, Jean +1
Mathematics · #11G30 #11N25 #11P05 #12E30 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1404.2849

openalex publication_date 2014/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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