17 citations · 44 across the 20 of their papers we have counts for
25 papers
Vertex operator algebra bundles on modular curves and their associated modular forms
Daniel Barake, Owen Chuchman, Cameron Franc +2
This paper describes the vector bundle on the elliptic modular curve that is associated to a vertex operator algebra (VOA) or more generally a quasi-vertex operator algebra (QV…
An Improved Lower Bound on the Image of the 2-adic Character Map for the Heisenberg Algebra via Modular Linear Differential Equations
Daniel Barake, Cameron Franc
We describe families of MLDEs whose solutions are modular forms of level one that converge, -adically, to a Hauptmodul on by using a theorem of Serre. Then, we apply th…
The moduli space of representations of the modular group into
Angelica Babei, Andrew Fiori, Cameron Franc
In this paper we construct a large four-dimensional family of representations of the modular group into . Precisely, this family is an etale cover of degree of an open su…
Density formulas for -adically bounded primes for hypergeometric series with rational and quadratic irrational parameters
Cameron Franc, Nathan Heisz, Hannah Nardone
We study densities of -adically bounded primes for hypergeometric series in two cases: the case of generalized hypergeometric series with rational parameters, and the case of $_…
Invitation to -adic vertex algebras
Cameron Franc, Geoffrey Mason
An overview of the authors' ideas about the process of completing a -adically normed space in the setting of vertex operator algebras. We focus in particular on the -adic Hei…
On -adic modularity in the -adic Heisenberg algebra
Cameron Franc, Geoffrey Mason
We establish existence theorems for the image of the normalized character map of the -adic Heisenberg algebra taking values in the algebra of Serre -adic modular forms $M…
Characters in p-adic Heisenberg and Lattice Vertex Operator Algebras
Daniel Barake, Cameron Franc
We study characters of states in -adic vertex operator algebras. In particular, we show that the image of the character map for both the -adic Heisenberg and -adic lattice…
p-adic vertex operator algebras
Cameron Franc, Geoffrey Mason
We postulate axioms for a chiral half of a nonarchimedean 2-dimensional bosonic conformal field theory, that is, a vertex operator algebra in which a p-adic Banach space replaces t…
Families of -congruence subgroups of the modular group
Angelica Babei, Andrew Fiori, Cameron Franc
We introduce and study families of finite index subgroups of the modular group that generalize the congruence subgroups. Such groups, termed -congruence subgroups, are obtained…
Character Vectors of Strongly Regular Vertex Operator Algebras
Cameron Franc, Geoffrey Mason
We summarize interactions between vertex operator algebras and number theory through the lens of Zhu theory. The paper begins by recalling basic facts on vertex operator algebras (…
Eisenstein Metrics
Cameron Franc
We study families of metrics on automorphic vector bundles associated to representations of the modular group. These metrics are defined using an Eisenstein series construction. We…
The unbounded denominator conjecture for the noncongruence subgroups of index
Andrew Fiori, Cameron Franc
We study modular forms for the minimal index noncongruence subgroups of the modular group. Our main theorem is a proof of the unbounded denominator conjecture for these groups, and…
Classification of some vertex operator algebras of rank 3
Cameron Franc, Geoffrey Mason
We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differen…
Nonabelian Hodge theory and vector valued modular forms
Cameron Franc, Steven Rayan
We examine the relationship between nonabelian Hodge theory for Riemann surfaces and the theory of vector valued modular forms. In particular, we explain how one might use this rel…
Constructions of vector-valued modular forms of rank four and level one
Cameron Franc, Geoff Mason
This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible re…
Densities of bounded primes for hypergeometric series with rational parameters
Cameron Franc, Brandon Gill, Jason Goertzen +2
The set of primes where a hypergeomeric series with rational parameters is -adically bounded is known by [10] to have a Dirichlet density. We establish a formula for this Dirich…
On unbounded denominators and hypergeometric series
Cameron Franc, Terry Gannon, Geoffrey Mason
We study the question of when the coefficients of a hypergeometric series are p-adically unbounded for a given rational prime p. Our first main result is a necessary and sufficient…
Vector bundles and modular forms for Fuchsian groups of genus zero
Luca Candelori, Cameron Franc
This article lays the foundations for the study of modular forms transforming with respect to representations of Fuchsian groups of genus zero. More precisely, we define geometrica…
Generating weights for the Weil representation attached to an even order cyclic quadratic module
Luca Candelori, Cameron Franc, Gene S. Kopp
We develop geometric methods to study the generating weights of free modules of vector valued modular forms of half-integral weight, taking values in a complex representation of th…
On the structure of modules of vector valued modular forms
Cameron Franc, Geoffrey Mason
If denotes a finite dimensional complex representation of , then it is known that the module of vector valued modular forms for is free an…
Vector valued modular forms and the modular orbifold of elliptic curves
Luca Candelori, Cameron Franc
This paper presents the theory of holomorphic vector valued modular forms from a geometric perspective. More precisely, we define certain holomorphic vector bundles on the modular…
Three-dimensional imprimitive representations of the modular group and their associated modular forms
Cameron Franc, Geoffrey Mason
This paper uses previous results of the authors on vector-valued modular forms to study certain non-congruence modular forms. We prove that these forms have unbounded denominators,…
Hypergeometric series, modular linear differential equations, and vector-valued modular forms
Cameron Franc, Geoffrey Mason
We survey the theory of vector-valued modular forms and their connections with modular differential equations and Fuchsian equations over the three-punctured sphere. We present a n…
Fourier coefficients of vector-valued modular forms of dimension 2
Cameron Franc, Geoffrey Mason
We prove the following theorem. Suppose that is a 2-dimensional vector-valued modular form on whose component functions have rational Fourier co…