3 papers
math.NT2024
On Drinfeld modular curves for SL(2)
Jesse Franklin, Sheng-Yang Kevin Ho, Mihran Papikian
We study the Drinfeld modular curves arising from the Hecke congruence subgroups of . Using a combinatorial method of Gekeler and Nonnengardt, we ob…
math.NT2023
Section Rings of -Divisors on Genus Curves
Michael Cerchia, Jesse Franklin, Evan O'Dorney
We compute generators and relations for the section ring of a rational divisor on an elliptic curve. Our technique generalizes the work of O'Dorney (in genus zero) and Voight--Zure…
math.NT2023
The Geometry of Drinfeld Modular Forms
Jesse Franklin
We give a geometric perspective on the algebra of Drinfeld modular forms for congruence subgroups $Γ\leq \GL_2(\bbF_q[T]).$ In particular, we describe an isomorphism between the se…