Indefinite theta series and generalized error functions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-11

AUTHORS

Sergei Alexandrov, Sibasish Banerjee, Jan Manschot, Boris Pioline

ABSTRACT

Theta 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... »

PAGES

3927-3972

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00029-018-0444-9

DOI

http://dx.doi.org/10.1007/s00029-018-0444-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107317675


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40 schema:description Theta 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.
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