3 papers
math.NT2026
Prime-power congruences for level-one eigenforms
Nadim Rustom
We study prime-power congruences for the prime-to-\(p\) Hecke eigensystems of normalized cuspidal level-one eigenforms as the weight varies, and we address the problem of classifyi…
math.NT2020
Eisenstein series, p-adic modular functions, and overconvergence
Ian Kiming, Nadim Rustom
Let be a prime . We establish explicit rates of overconvergence for members of the "Eisenstein family", notably for the -adic modular function $V(E_{(1,0)}^{\ast})/E_…
math.NT2018
Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4
Ian Kiming, Nadim Rustom
We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whe…