Mock modular forms and class number relations

DOI10.1186/2197-9847-1-6zbMath1352.11049arXiv1305.5122OpenAlexW2071931968WikidataQ59394449 ScholiaQ59394449MaRDI QIDQ290115

Michael H. Mertens

Publication date: 1 June 2016

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.5122

zbMATH Keywords

mock modular formAppell-Lerch sumclass number relation

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Fourier coefficients of automorphic forms (11F30) Class numbers of quadratic and Hermitian forms (11E41)

Related Items (12)

Eichler-Selberg type identities for mixed mock modular forms ⋮ Higher Siegel theta lifts on Lorentzian lattices, harmonic Maass forms, and Eichler-Selberg type relations ⋮ Theta lifts for Lorentzian lattices and coefficients of mock theta functions ⋮ Polar harmonic Maaß forms and holomorphic projection ⋮ Local Maass forms and Eichler-Selberg relations for negative-weight vector-valued mock modular forms ⋮ Poincaré square series of small weight ⋮ Optimal estimates for an average of Hurwitz class numbers ⋮ Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series ⋮ Traces of CM values and cycle integrals of polyharmonic Maass forms ⋮ On the trace formula for Hecke operators on congruence subgroups. II ⋮ Vector-valued Hirzebruch-Zagier series and class number sums ⋮ Mock modular Eisenstein series with Nebentypus

Cites Work

• The theory of Jacobi forms
• Elliptic curves, modular forms, and sums of Hurwitz class numbers
• The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004
• 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
• Rank-crank type PDE's and non-holomorphic Jacobi forms
• The \(f(q)\) mock theta function conjecture and partition ranks
• On modular forms of half integral weight
• Overpartitions and class numbers of binary quadratic forms
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