Ontology type: schema:ScholarlyArticle Open Access: True
2018-11
AUTHORSSergei Alexandrov, Sibasish Banerjee, Jan Manschot, Boris Pioline
ABSTRACTTheta series for lattices with indefinite signature (n+,n-) arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case (n+=1), but have remained obscure when n+≥2. Using a higher-dimensional generalization of the usual (complementary) error function, discovered in an independent physics project, we construct the modular completion of a class of ‘conformal’ holomorphic theta series (n+=2). As an application, we determine the modular properties of a generalized Appell–Lerch sum attached to the lattice A2, which arose in the study of rank 3 vector bundles on P2. The extension of our method to n+>2 is outlined. More... »
PAGES3927-3972
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DOIhttp://dx.doi.org/10.1007/s00029-018-0444-9
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