Overpartitions and class numbers of binary quadratic forms

Details Overpartitions and class numbers of binary quadratic forms Overpartitions and class numbers of binary quadratic forms

2007-12-04

arxiv.org/abs/0712.0631v1

Mathematics

Number Theory

9 pages

Scientific paper

We show that the Zagier-Eisenstein series shares its non-holomorphic part
with certain weak Maass forms whose holomorphic parts are generating functions
for overpartition rank differences. This has a number of consequences,
including exact formulas, asymptotics, and congruences for the rank differences
as well as $q$-series identities of the mock theta type.

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