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2 results

  • PARTIAL INDEFINITE THETA IDENTITIES

  • Part of
  • BYUNGCHAN KIM, JEREMY LOVEJOY
  • Journal:
    Journal of the Australian Mathematical Society / Volume 102 / Issue 2 / April 2017
    Published online by Cambridge University Press:
    19 September 2016, pp. 255-289
    Print publication:
    April 2017
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  • Using a result of Warnaar, we prove a number of single- and multi-sum identities in the spirit of Ramanujan’s partial theta identities, but with partial indefinite binary theta functions in the role of partial theta functions. We also calculate the corresponding residual identities and use a result of Ji and Zhao to recast our identities in terms of indefinite ternary theta functions.

  • On a completed generating function of locally harmonic Maass forms

  • Part of
  • Kathrin Bringmann, Ben Kane, Sander Zwegers
  • Journal:
    Compositio Mathematica / Volume 150 / Issue 5 / May 2014
    Published online by Cambridge University Press:
    26 March 2014, pp. 749-762
    Print publication:
    May 2014
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  • While investigating the Doi–Naganuma lift, Zagier defined integral weight cusp forms $f_D$ which are naturally defined in terms of binary quadratic forms of discriminant $D$. It was later determined by Kohnen and Zagier that the generating function for the function $f_D$ is a half-integral weight cusp form. A natural preimage of $f_D$ under a differential operator at the heart of the theory of harmonic weak Maass forms was determined by the first two authors and Kohnen. In this paper, we consider the modularity properties of the generating function of these preimages. We prove that although the generating function is not itself modular, it can be naturally completed to obtain a half-integral weight modular object.