Cécile Armana

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math.NT2026

A computational approach to Drinfeld modules

CÃ©cile Armana, Elena Berardini, Xavier Caruso +3

This survey provides a practical and algorithmic perspective on Drinfeld modules over $F_{q} [T]$ . Starting with the construction of the Carlitz module, we present Drinfeld mo…

math.NT2024

Ogg's conjectures over function fields

CÃ©cile Armana, Sheng-Yang Kevin Ho, Mihran Papikian

In the early 1970s, Andrew Ogg made several conjectures about the rational torsion points of elliptic curves over $Q$ and the Jacobians of modular curves. These conjecture…

math.NT2024

Non-perfect pairings between Hecke algebra and modular forms over function fields

CÃ©cile Armana

We study two analogs, for modular forms over $F_{q} (T)$ , of the pairing between Hecke algebra and cusp forms given by the first coefficient in the expansion. For Drinfeld…

math.NT2024

Drinfeld singular moduli, hyperbolas, units

Let $q \geq 2$ be a prime power and consider Drinfeld modules of rank 2 over $F_{q} [T]$ . We prove that there are no points with coordinates being Drinfeld singular moduli, on…