Counting solvable 𝒮-unit equations and linear recurrence sequences with zeros
Abstract
We show that only a rather small proportion of linear equations are solvable in elements of a fixed finitely generated subgroup of a multiplicative group of a number field. The argument is based on modular techniques combined with a classical idea of P. Erdős (1935). We then use similar ideas to get a tight upper bound on the number of linear recurrence sequences which attain a zero value.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Analytic Number Theory Research
Advanced Algebra and Geometry
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 16 January 2026
- Language
- EN