Related papers: Zagier's weight $3/2$ mock modular form

The mock theta conjectures are ten identities involving Ramanujan's fifth-order mock theta functions. The conjectures were proven by Hickerson in 1988 using q-series methods. Using methods from the theory of harmonic Maass forms,…

We show that the generating series of traces of reciprocal singular moduli is a mixed mock modular form of weight $3/2$ whose shadow is given by a linear combination of products of unary and binary theta functions. To prove these results,…

This article describes results of joint work with Michael Rapoport and Tonghai Yang. First, we construct an modular form \phi(\tau) of weight 3/2 valued in the arithmetic Chow group of the arithmetic surface M attached toa Shimura curve…

Using holomorphic projection, we work out a parametrization for all relations of products (resp. Rankin-Cohen brackets) of weight $\tfrac 32$ mock modular forms with holomorphic shadow and weight $\tfrac 12$ modular forms in the spirit of…

In a private communication, K. Ono conjectured that any mock theta function of weight 1/2 or 3/2 can be congruent modulo a prime $p$ to a weakly holomorphic modular form for just a few values of $p$. In this paper we describe when such a…

We prove an abstract modularity result for classes of Heegner divisors in the generalized Jacobian of a modular curve associated to a cuspidal modulus. Extending the Gross-Kohnen-Zagier theorem, we prove that the generating series of these…

We show that some $q$-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion…

The primary goal of this paper is to construct the basis of the space of weight 3/2 mock modular forms which is an extension of the Borcherd-Zagier basis of weight 3/2 weakly holomorphic modular forms. The shadows of the members of this…

In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock…

Sander Zwegers showed that Ramanujan's mock theta functions are $q$-hypergeometric series, whose $q$-expansion coefficients are half of the Fourier coefficients of a non-holomorphic modular form. George Andrews, Henri Cohen, Freeman Dyson,…

We compute the Moore-Witten regularized u-plane integral on CP^2, and we confirm their conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP^2. We prove this conjecture using the theory of mock theta…

Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous different topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions near roots of unity. These are…

In this paper, we explicitly construct mock modular forms whose shadows are Eisenstein series of arbitrary integral and half-integral weight, level and character at the cusps $\infty$ and $0$. As an application, we give explicit…

At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. Many of Ramanujan's mock theta functions can be written in…

Zagier proved that the generating series for the traces of singular moduli is a \textit{weakly holomorphic} modular form of weight 3/2 on $\Gamma_0(4)$. Bruinier and Funke extended the results of Zagier to modular curves of arbitrary genus.…

In this paper we construct a modular form f of weight one attached to an imaginary quadratic field K. This form, which is non-holomorphic and not a cusp form, has several curious properties. Its negative Fourier coefficients are non-zero…

In this paper we add to the literature on the combinatorial nature of the mock theta functions, a collection of curious $q$-hypergeometric series introduced by Ramanujan in his last letter to Hardy in 1920, which we now know to be important…

In this paper we study the characters of N=3 superconformal modules by using the Zwegers' theory on modification of mock theta functions.

We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for $\Gamma_0(4)$ with Kohnen's plus condition and…

For any number $m \equiv 0,1 \, (4)$ we correct the generating function of Hurwitz class number sums $\sum_r H(4n - mr^2)$ to a modular form (or quasimodular form if $m$ is a square) of weight two for the Weil representation attached to a…