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Mock Jacobi forms in basic hypergeometric series

Part of: Discontinuous groups and automorphic forms Basic hypergeometric functions Combinatorics

Published online by Cambridge University Press:  01 May 2009

Soon-Yi Kang
Soon-Yi Kang*
Affiliation:
Korea Advanced Institute for Science and Technology, Daejeon 305-701, Korea (email: s2kang@kaist.ac.kr)
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Abstract

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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.

Keywords

basic hypergeometric seriesmock Jacobi formsmock modular formsweakly holomorphic modular formsranks and cranks of partitions

MSC classification

Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F50: Jacobi forms 05A17: Partitions of integers 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 3 , May 2009 , pp. 553 - 565
Copyright
Copyright © Foundation Compositio Mathematica 2009

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