Indefinite theta series and generalised error functions
Citation:
Sergey Alexandrov, Sibasish Banerjee, Jan Manschot, Boris Pioline, Indefinite theta series and generalised error functions, Selecta Mathematica, 2018, 3927 - 3972Abstract:
Theta series for lattices with indefinite signature (
n
+
,n
−
) arise in many areas of
mathematics including representation theory and enumerative algebraic geometry. Their mod-
ular 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 A
2
, which arose in
the study of rank 3 vector bundles on
P
2
. The extension of our method to
n
+
>
2 is outlined.
Author's Homepage:
http://people.tcd.ie/manschojDescription:
PUBLISHED
Author: Manschot, Jan
Type of material:
Journal ArticleSeries/Report no:
Selecta MathematicaAvailability:
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Theta seriesMetadata
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