Wieferich and Mersenne primes for function fields

2025/12/08 by Lucas, Alexis
Mathematics · #11A99 #11G09 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · doi:10.48550/arxiv.2512.08060

openalex publication_date 2025/12/08 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

We study properties of recently introduced Wieferich primes for Drinfeld modules, as their relation with Fermat equations and finitess or non-finiteness of their number. We also introduce Mersenne numbers for Drinfeld modules, and study the links between these two notions.

Citations

• Wieferich primes in number fields and the conjectures of Ankeny--Artin--Chowla and Mordell
• Une supercongruence de Wilson exacte pour les premiers d'Artin-Schreier de F_p[t] (An exact Wilson supercongruence for Artin-Schreier primes in F_p[t])
• Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields
• Arithmetic of Units in F_q[T]

Related

• Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields
• Une supercongruence de Wilson exacte pour les premiers d'Artin-Schreier de F_p[t] (An exact Wilson supercongruence for Artin-Schreier primes in F_p[t])
• ABC Implies There are Infinitely Many non-Fibonacci-Wieferich Primes - An Application of ABC Conjecture over Number Fields
• Towers of Function Fields over Non-prime Finite Fields
• Wall's Conjecture and the ABC Conjecutre