Mock theta functions and weakly holomorphic modular forms modulo 2 and 3

Mock Theta Functions and Quantum Modular Forms

Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function f (q), Ramanujan claims that as q approaches an even-order 2k root of unity, we have f (q)− (−1)(1− q)(1− q)(1− q) · · · (1− 2q+ 2q − · · ·)= O(1). We prove Ramanujan’s claim as a special case of a more general result. The implied constants in Ramanuja...

Holomorphic projections and Ramanujan's mock theta functions.

We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan's mock theta functions.

Mock Theta Functions, Ranks, and Maass Forms

Mock modular forms and geometric theta functions for indefinite quadratic forms

Mock modular forms are central objects in the recent discoveries of new instances of Moonshine. In this paper, we discuss the construction of mixed mock modular forms via integrals of theta series associated to indefinite quadratic forms. In particular, in this geometric setting, we realize Zwegers’ mock theta functions of type ( p, 1) as line integrals in hyperbolic p-space.

Odd Coefficients of Weakly Holomorphic Modular Forms

s 1. Fisseha Abebe, Clark Atlanta University Distance Metric for Protein Partitions The composition of proteins in terms of amino-acid sequences within three protein theoretical families: serine, leucine, and valine, with respective sizes of 8, 7, and 5 amino acids, have been studied using combinatorial methods. All possible partitions are examined, and a metric is defined to measure the distan...