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http://dx.doi.org/10.4134/BKMS.b160813

MOCK THETA FUNCTIONS OF ORDER 2 AND THEIR SHADOW COMPUTATIONS  

Kang, Soon-Yi (Department of Mathematics Kangwon National University)
Swisher, Holly (Department of Mathematics Kangwon National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 2155-2163 More about this Journal
Abstract
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.
Keywords
basic hypergeometric series; second order mock theta functions; shadows of mock modular forms; mock modular forms;
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