Mock Jacobi forms in basic hypergeometric series

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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.
Publisher
LONDON MATH SOC
Issue Date
2009
Language
English
Article Type
Article
Keywords

MODULAR-FORMS; THETA; PARTITION; RANKS

Citation

COMPOSITIO MATHEMATICA, v.145, no.3, pp.553 - 565

ISSN
0010-437X
DOI
10.1112/S0010437X09004060
URI
http://hdl.handle.net/10203/94547
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