Mock Jacobi forms in basic hypergeometric series

Details Mock Jacobi forms in basic hypergeometric series Mock Jacobi forms in basic hypergeometric series

2008-06-11

arxiv.org/abs/0806.1878v2

Mathematics

Number Theory

13 pages

Scientific paper

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 points and multiplied by suitable powers of $q$. And we prove that certain linear sums of $q$-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.

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