8 citations · 24 across the 14 of their papers we have counts for
15 papers
Eisenstein series, -adic modular functions, and overconvergence, II
Ian Kiming, Nadim Rustom
Let be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular functions of the form $\frac{E_k^…
A Conjecture of Coleman on the Eisenstein Family
Bryan W. Advocaat, Ian Kiming, Gabor Wiese
We prove for primes a conjecture of Coleman on the analytic continuation of the family of modular functions derived from the family of Eisen…
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_…
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…
On certain finiteness questions in the arithmetic of modular forms
Ian Kiming, Nadim Rustom, Gabor Wiese
We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We lin…
On the theta operator for modular forms modulo prime powers
Imin Chen, Ian Kiming
We consider the classical theta operator on modular forms modulo and level prime to where is a prime greater than 3. Our main result is that mod wil…