Doron Shafrir

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20242026

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math.NT2026

Skolem-Mahler-Lech in rings of positive characteristic: a shorter proof and a multi-dimensional generalization

Ruiwen Dong, Doron Shafrir

Let $R$ be a commutative ring and $f (a_{1}, \dots, a_{n}) = \sum_{i = 1}^{k} r_{i 1}^{a_{1}} \dots r_{in}^{a_{n}} m_{i}$ be a linear-exponential map over an $R$ -module $M$ . Dong and Shafrir (20…

math.NT2025

S-unit equations in modules and linear-exponential Diophantine equations

Ruiwen Dong, Doron Shafrir

Let $T$ be a positive integer, and $M$ be a finitely presented module over the Laurent polynomial ring $Z_{/ T} [X_{1}^{\pm}, \dots, X_{N}^{\pm}]$ . We consider S-unit…