Mock theta functions of order 2 and their shadow computations
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2155-2163
Published online November 30, 2017
Soon-Yi Kang, Holly Swisher
Kangwon National University, Oregon State University
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
MSC numbers : 11F37, 33D15
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