Back to matchesWe found a matchYour institution may have access to this item. Find your institution then sign in to continue.TitleDifferential operators on polar harmonic Maass forms and elliptic duality.AuthorsBringmann, Kathrin; Jenkins, Paul; Kane, BenAbstractIn this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincaré series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which are similar to the properties known for Fourier coefficients of harmonic Maass forms and weakly holomorphic modular forms.SubjectsDIFFERENTIAL operators; POINCARE series; MODULAR forms; CUSP forms (Mathematics); ELLIPTIC operatorsPublicationQuarterly Journal of Mathematics, 2019, Vol 70, Issue 4, p1181ISSN0033-5606Publication typeArticleDOI10.1093/qmath/haz009