6 papers
A class formula for effective Anderson motives
Xavier Caruso, Quentin Gazda, Alexis Lucas
We establish a class formula with variable for arbitrary effective Anderson motives. This pursues the pioneering work of Taelman and extends the scope of the work of Angl{è}s-Ngo D…
Logarithmic-depth quantum state preparation of polynomials
Baptiste Claudon, Alexis Lucas, Jean-Philip Piquemal +2
Quantum state preparation is a central primitive in many quantum algorithms, yet it is generally resource intensive, with efficient constructions known only for structured families…
Wieferich and Mersenne primes for function fields
Alexis Lucas
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 in…
A P-adic class formula for Anderson t-modules
Alexis Lucas
Let be a monic prime of , we define the -adic -series associated with Anderson -modules and prove a -adic class formula à la Taelman linking a -a…
Wieferich primes for Drinfeld modules
Xavier Caruso, Quentin Gazda, Alexis Lucas
The aim of this paper is to discuss the notion of Wieferich primes in the context of Drinfeld modules. Our main result is a surprising connection between the proprety of a monic ir…
Purity and almost strict purity of Anderson t-modules
Alexis Lucas
We study the relations between the notion of purity of a t-module introduced by Anderson and that of almost strict purity for a t-module introduced by Namoijam and Papanikolas (con…