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Overpartition -rank differences, class number relations, and vector-valued mock Eisenstein series
We prove that the generating function of overpartition -rank differences
is, up to coefficient signs, a component of the vector-valued mock Eisenstein
series attached to a certain quadratic form. We use this to compute analogs of
the class number relations for -rank differences. As applications we split
the Kronecker-Hurwitz relation into its "even" and "odd" parts and calculate
sums over Hurwitz class numbers of the form .Comment: 13 pages. v2 includes a notation and background section and changes
some notatio
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