Wieferich and Mersenne primes for function fields
Alexis Lucas
TL;DR
This paper explores properties of Wieferich primes and Mersenne numbers within the context of Drinfeld modules, examining their relationships with Fermat equations and the finiteness of their sets.
Contribution
It introduces Mersenne numbers for Drinfeld modules and investigates the connections between Wieferich primes and Mersenne numbers in this setting.
Findings
Properties of Wieferich primes for Drinfeld modules are characterized.
Relationships between Wieferich primes and Fermat equations are analyzed.
Links between Mersenne numbers and Wieferich primes are established.
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.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Algebraic Geometry and Number Theory