158 research outputs found
The tenth order mock theta functions revisited
In this paper we consider the first four of the eight identities between the
tenth order mock theta functions, found in Ramanujan's lost notebook. These
were originally proved by Choi. Here we give an alternative (much shorter)
proof.Comment: 11 pages; preprint, submitted for publicatio
On the Fourier coefficients of negative index meromorphic Jacobi forms
In this paper, we consider the Fourier coefficients of meromorphic Jacobi
forms of negative index. This extends recent work of Creutzig and the first two
authors for the special case of Kac-Wakimoto characters which occur naturally
in Lie theory, and yields, as easy corollaries, many important PDEs arising in
combinatorics such as the famous rank-crank PDE of Atkin and Garvan. Moreover,
we discuss the relation of our results to partial theta functions and quantum
modular forms as introducted by Zagier, which together with previous work on
positive index meromorphic Jacobi forms illuminates the general structure of
the Fourier coefficients of meromorphic Jacobi forms.Comment: 13 pages, minor change
Mock Jacobi forms in basic hypergeometric series
We show that some -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 points and multiplied by suitable powers of . And we
prove that certain linear sums of -series are weakly holomorphic modular
forms of weight 1/2 due to annihilation of mock Jacobi forms or completion by
mock Jacobi forms. As an application, we obtain a relation between the rank and
crank of a partition.Comment: 13 page
Rank-Crank type PDE's for higher level Appell functions
In this paper we consider level l Appell functions, and find a partial
differential equation for all odd l. For l=3 this recovers the Rank-Crank PDE,
found by Atkin and Garvan, and for l=5 we get a similar PDE found by Garvan.Comment: Preprint, 10 page
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