4 citations · 5 across the 6 of their papers we have counts for
6 papers
Logarithmic vector-valued modular forms and polynomial-growth estimates of their Fourier coefficients
Marvin Knopp, Geoffrey Mason
We establish (Theorem 3.6) polynomial-growth estimates for the Fourier coefficients of holomorphic logarithmic vector-valued modular forms.
Individual Closed Horocyclic Orbits on the Modular Surface
Marvin Knopp, Mark Sheingorn
We track the trajectories of individual horocycles on the modular surface. Our tracking is constructive, and we thus \emph{effectively} establish topological transitivity and even…
Vector-valued modular forms with an unnatural boundary
Marvin Knopp, Geoffrey Mason
We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.
Individual Horocyclic Orbits on , Closed and Otherwise
Marvin Knopp, Mark Sheingorn
This paper endeavors to track the trajectories of individual horocycles on \modsurf. It is far more common to study \emph{sets} of such trajectories, seeking some asymptotic behavi…
Horocyclic Orbits on $Γ(1)\frontslash\mathcal{H}$, \ Closed and Otherwise
Marvin Knopp, Mark Sheingorn
This paper studies certain horocyclic orbits on $Γ(1)\frontslash\mathcal{H}$. In the first instance we examine horocycles defined using the pencil of circles whose common point (in…
Logarithmic vector-valued modular forms
Marvin Knopp, Geoffrey Mason
We consider logarithmic vector- and matrix-valued modular forms of integral weight associated with a -dimensional representation o…