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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.
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참고문헌 (19)
참고문헌 신청
A. Folsom / 2013 / Mock theta functions and quantum modular forms / Forum Math. Pi 1 : 27 ~
A. Folsom / 2016 / Quantum mock modular forms arising from eta-theta fnctions / Res. Number Theory 2
B. Gordon / 2012 / A survey of classical mock theta functions, Par-titions, q-Series, and Modular Forms / Springer : 95 ~ 144
D. Zagier / 2009 / Ramanujan's mock theta functions and their applications (after Zwegers and Ono-Bringmann) / Seminaire Bourbaki 2007/2008 (326)
D. Zagier / 2010 / Quantum Modular Forms / In Quanta of Maths: Conference in honor of Alain Connes, Clay Math. Proc. 11 : 659 ~ 675
A. Folsom / 2016 / Quantum mock modular forms arising from eta-theta fnctions / Res. Number Theory 2
B. Gordon / 2012 / A survey of classical mock theta functions, Par-titions, q-Series, and Modular Forms / Springer : 95 ~ 144
D. Zagier / 2009 / Ramanujan's mock theta functions and their applications (after Zwegers and Ono-Bringmann) / Seminaire Bourbaki 2007/2008 (326)
D. Zagier / 2010 / Quantum Modular Forms / In Quanta of Maths: Conference in honor of Alain Connes, Clay Math. Proc. 11 : 659 ~ 675
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