Overpartitions and real quadratic fields

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DYSON'S RANK, OVERPARTITIONS, AND WEAK MAASS FORMS (2007, background): “To give a few specific examples, the combinatorial theory of overpartitions leads to natural and straightforward bijective proofs of q-series identities like Ramanujan’s 1ψ1 summation [12, 33]; in the theory of symmetric functions in superspace, overpartitions play the role that partitions play in t”
AN INFINITE FAMILY OF OVERPARTITION CONGRUENCES MODULO 12 (2005, background): “The function p(n) has been considered recently by a number of mathematicians; please see [1, 2, 3, 4, 5, 6, 7, 8].”
Arithmetic Properties of Overpartitions into Odd Parts (2006, background): “S. Corteel, J. Lovejoy, and A. Yee, Overpartitions and generating functions for generalized Frobenius partitions, Trends Math.”
RANK DIFFERENCES FOR OVERPARTITIONS (2007, background): “Overpartitions (often under other names) naturally arise in diverse areas of mathematics where partitions already occur, such as mathematical physics [15, 16], symmetric functions [4, 13], representation theory [20], and algebraic number theory [21, 23].”