Overpartitions and class numbers of binary quadratic forms

DOI10.1073/pnas.0900783106zbMath1202.11029arXiv0712.0631OpenAlexW2071098578WikidataQ37153632 ScholiaQ37153632MaRDI QIDQ3066188

Kathrin Bringmann, Jeremy Lovejoy

Publication date: 9 January 2011

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0631

zbMATH Keywords

congruencesharmonic Maass formmock theta functionDyson's rankZagier-Eisenstein series

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Class numbers of quadratic and Hermitian forms (11E41) Analytic theory of partitions (11P82)

Related Items (22)

Lambert series and conjugacy classes in \(\mathrm{GL}\) ⋮ Indefinite theta series and generalized error functions ⋮ Mock modular forms and class number relations ⋮ The first positive rank and crank moments for overpartitions ⋮ Eichler-Selberg type identities for mixed mock modular forms ⋮ Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers ⋮ The Corners of Core Partitions ⋮ Poincaré square series of small weight ⋮ Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms ⋮ OVERPARTITIONS RELATED TO THE MOCK THETA FUNCTION ⋮ Vector-valued Eisenstein series of small weight ⋮ Mock modular forms as $p$-adic modular forms ⋮ An overpartition analogue of the \(q\)-binomial coefficients ⋮ Overpartitions and ternary quadratic forms ⋮ On the asymptotic behavior of Kac-Wakimoto characters ⋮ Perspectives on mock modular forms ⋮ \(M_2\)-rank of overpartitions and harmonic weak Maass forms ⋮ Mock modularity of the \(M_{d}\)-rank of overpartitions ⋮ Overpartitions with restricted odd differences ⋮ On the number of partitions with designated summands ⋮ Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series ⋮ Automorphic properties of generating functions for generalized odd rank moments and odd Durfee symbols

Cites Work

• Rank and conjugation for a second Frobenius representation of an overpartition
• Partitions and indefinite quadratic forms.
• q-identities for Maass waveforms
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• On two geometric theta lifts
• Some observations on Dyson's new symmetries of partitions
• The \(f(q)\) mock theta function conjecture and partition ranks

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