| dc.contributor.author | Manschot, Jan | en |
| dc.date.accessioned | 2018-01-24T16:46:42Z | |
| dc.date.available | 2018-01-24T16:46:42Z | |
| dc.date.issued | 2018 | en |
| dc.date.submitted | 2018 | en |
| dc.identifier.citation | Sergey Alexandrov, Sibasish Banerjee, Jan Manschot, Boris Pioline, Indefinite theta series and generalised error functions, Selecta Mathematica, 2018, 3927 - 3972 | en |
| dc.identifier.other | Y | en |
| dc.description | PUBLISHED | en |
| dc.description.abstract | 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. | en |
| dc.format.extent | 3927 | en |
| dc.format.extent | 3972 | en |
| dc.language.iso | en | en |
| dc.relation.ispartofseries | Selecta Mathematica | en |
| dc.rights | Y | en |
| dc.subject | Theta series | en |
| dc.title | Indefinite theta series and generalised error functions | en |
| dc.type | Journal Article | en |
| dc.type.supercollection | scholarly_publications | en |
| dc.type.supercollection | refereed_publications | en |
| dc.identifier.peoplefinderurl | http://people.tcd.ie/manschoj | en |
| dc.identifier.rssinternalid | 122618 | en |
| dc.rights.ecaccessrights | openAccess | |
| dc.identifier.rssuri | https://arxiv.org/abs/1606.05495 | en |
| dc.identifier.orcid_id | 0000-0002-6506-7084 | en |
| dc.identifier.uri | http://hdl.handle.net/2262/82265 | |
