• 제목/요약/키워드: shadows of mock modular forms

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MOCK THETA FUNCTIONS OF ORDER 2 AND THEIR SHADOW COMPUTATIONS

  • Kang, Soon-Yi;Swisher, Holly
    • 대한수학회보
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    • 제54권6호
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    • pp.2155-2163
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    • 2017
  • Zwegers showed that a mock theta function can be completed to form essentially a real analytic modular form of weight 1/2 by adding a period integral of a certain weight 3/2 unary theta series. This theta series is related to the holomorphic modular form called the shadow of the mock theta function. In this paper, we discuss the computation of shadows of the second order mock theta functions and show that they share the same shadow with a mock theta function which appears in the Mathieu moonshine phenomenon.

QUANTUM MODULARITY OF MOCK THETA FUNCTIONS OF ORDER 2

  • Kang, Soon-Yi
    • Korean Journal of Mathematics
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    • 제25권1호
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    • pp.87-97
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    • 2017
  • In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.