Rank two false theta functions and Jacobi forms of negative definite matrix index

Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters

Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters Kathrin Bringmann,1,a) Amanda Folsom,2,b) and Antun Milas3,c) 1Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany 2Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts 01002, USA 3Department of Mathematics and Statistics, S...

Factorization of rank two theta functions

FALSE, PARTIAL, AND MOCK JACOBI THETA FUNCTIONS AS q-HYPERGEOMETRIC SERIES

to add 1. Curious q-series Identities Since Rogers [32] introduced the false theta functions, they have played a curious role in the theory of partitions (see for instance [1, 2, 12]). Andrews [3] defined a false theta function as any series of the shape ∑ n∈Z(±1)q 2+`n that has different signs for the nonzero terms. For example, Rogers proved (1.1) ∑ j≥0 q j(3j+1) 2 − ∑ j≤−1 q j(3j+1) 2 = ∑ j≥...

The Bailey Transform and False Theta Functions

An empirical exploration of five of Ramanujan’s intriguing false theta function identities leads to unexpected instances of Bailey’s transform which, in turn, lead to many new identities for both false and partial theta functions.

Jacobi Theta Functions over Number Fields

We use Jacobi theta functions to construct examples of Jacobi forms over number fields. We determine the behavior under modular transformations by regarding certain coefficients of the Jacobi theta functions as specializations of symplectic theta functions. In addition, we show how sums of those Jacobi theta functions appear as a single coefficient of a symplectic theta function. 2000 Mathemati...