Mock Jacobi forms in basic hypergeometric series

By Soon-Yi Kang. Compositio Mathematica, 2008

56 citations recorded by the source corpus.

Abstract 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. We also 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bdcc5447547e0f5186ba15355053538e6d651a63

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Citations in the corpus

The basic bilateral hypergeometric series and the mock theta functions (2011, background): “Kang [10] showed that”
Partial theta functions and mock modular forms as q-hypergeometric series (2011, background): “, for a definition of this term and more on mock modular forms and [18] for the shadow of g3).”
RANK DIFFERENCES FOR OVERPARTITIONS (2007, unknown): “!(q) = g3(q;q2): By Theorem 1.1 in [ 18 ], (5.2) xg2(x;q) =”
Unearthing the visions of a master: harmonic Maass forms and number theory (2008, methodology): “3 of [132]) two explicit families of weight 1/2 modular forms, described in terms of theta functions and Dedekind’s etafunction, which are sums of basic hypergeometric series.”