Related papers: Vector-Valued Rademacher Sums and Automorphic Inte…

We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe several applications, including the determination of…

We study rationality properties of geodesic cycle integrals of meromorphic modular forms associated to positive definite binary quadratic forms. In particular, we obtain finite rational formulas for the cycle integrals of suitable linear…

The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals.…

Using techniques from the theory of mock modular forms and harmonic Maass forms, especially Weierstrass mock modular forms, we establish several dimension formulas for certain strongly rational, holomorphic vertex operator algebras,…

A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…

In 1939 Rademacher derived a conditionally convergent series expression for the elliptic modular invariant, and used this expression- the first Rademacher sum - to verify its modular invariance. By generalizing Rademacher's approach we…

In this paper, we prove vector-valued higher depth quantum modular properties arising from characters of certain vertex algebras. We then find two-dimensional Mordell integral representations for their errors of modularity.

We introduce a method for producing vector-valued automorphic forms on unitary groups from scalar-valued ones. As an application, we construct an explicit example. Our strategy employs certain differential operators. It is inspired by work…

We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.

We present a dimension formula for spaces of vector-valued modular forms of integer weight in case the associated multiplier system has finite image, and discuss the weight distribution of the module generators of holomorphic and cusp…

In this paper, we use theta integrals to give a different construction of mock Maass forms studied by Sander Zwegers. With this method, we construct new real-analytic modular forms, whose Fourier coefficients are logarithms of algebraic…

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.

In this note, we explicitly construct mock modular forms with integral Fourier coefficients by evaluating regularized Petersson inner products involving their shadows, which are unary theta functions of weights 1/2 and 3/2 . In addition, we…

We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module $A$ has order $p$ or $2p$,…

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

We develop two structure theorems for vector valued Siegel modular forms for Igusa's subgroup \Gamma_2[2,4], the multiplier system induced by the theta constants and the representation Sym^2. In the proof, we identify some of these modular…

The holomorphic bootstrap attempts to classify rational conformal field theories. The straight ahead approach is hard to implement when the number of characters become large. We combine all characters of an RCFT to form a vector valued…

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 orbifold of generalized elliptic curves whose sections are…

In this paper we generalize the notion of logarithmic vector-valued modular form in order to give a general definition of matrix-valued Hilbert modular forms. We prove that they admit unique polynomial Fourier expansions and we build…

In this paper we present a method for constructing multiple-sum $q$-series for what is known as Mixed Mock Modular forms. We also present some multi-sum analogues of the Durfee identity, and discuss a construction of its combinatorial…