2009/04/09 by Soon-Yi Kang · 2 citations
Mathematics · #Advanced Mathematical Identities #Advanced Algebra and Geometry #Algebraic structures and combinatorial models
paper · pdf · doi:10.1112/s0010437x09004060
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.