The Ramanujan Journal

, Volume 36, Issue 1–2, pp 149–164 | Cite as

A mixed mock modular solution of the Kaneko–Zagier equation



The notion of mixed mock modular forms was recently introduced by Don Zagier. We show that certain solutions of the Kaneko–Zagier differential equation constitute simple yet non-trivial examples of this notion. That allows us to address a question posed by Kaneko and Koike on the (non)-modularity of these solutions.


Mixed mock modular forms Weak harmonic Maass forms Kaneko–Zagier differential equation 

Mathematics Subject Classification (2010)

11F12 11F37 



The author is very grateful to Masanobu Kaneko for enlightening discussions and explanations related to the mathematics around equation (KZ k ). Masanobu Kaneko also read a preliminary version of this note, corrected a bunch of miscalculations and inaccuracies, and filled in some details. The author wants to take this opportunity to express his gratitude to him for doing that. The author thanks the referee for helping to improve the exposition.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HawaiiHonoluluUSA

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