Work

Counting solvable $\mathcal S$-unit equations and linear recurrence sequences with zeros

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2503.03985

Authors: Ostafe, Alina, Pomerance, Carl, Shparlinski, Igor E.

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4416112197

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