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dc.contributor.author
von Pippich, Anna-Maria
dc.contributor.author
Schwagenscheidt, Markus
dc.contributor.author
Völz, Fabian
dc.date.accessioned
2021-03-24T10:21:41Z
dc.date.available
2021-03-09T08:03:59Z
dc.date.available
2021-03-09T08:07:01Z
dc.date.available
2021-03-24T10:21:41Z
dc.date.issued
2021-08
dc.identifier.issn
0022-314X
dc.identifier.issn
1096-1658
dc.identifier.other
10.1016/j.jnt.2021.01.010
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/473525
dc.identifier.doi
10.3929/ethz-b-000473525
dc.description.abstract
The classical Kronecker limit formula describes the constant term in the Laurent expansion at the first order pole of the non-holomorphic Eisenstein series associated to the cusp at infinity of the modular group. Recently, the meromorphic continuation and Kronecker limit type formulas were investigated for non-holomorphic Eisenstein series associated to hyperbolic and elliptic elements of a Fuchsian group of the first kind by Jorgenson, Kramer and the first named author. In the present work, we realize averaged versions of all three types of Eisenstein series for Γ0(N) as regularized theta lifts of a single type of Poincaré series, due to Selberg. Using this realization and properties of the Poincaré series we derive the meromorphic continuation and Kronecker limit formulas for the above Eisenstein series. The corresponding Kronecker limit functions are then given by the logarithm of the absolute value of the Borcherds product associated to a special value of the underlying Poincaré series.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier BV
en_US
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.title
Kronecker limit formulas for parabolic, hyperbolic and elliptic Eisenstein series via Borcherds products
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
dc.date.published
2021-02-23
ethz.journal.title
Journal of Number Theory
ethz.journal.volume
225
en_US
ethz.journal.abbreviated
J. Number Theory
ethz.pages.start
18
en_US
ethz.pages.end
58
en_US
ethz.size
41 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08799 - Imamoglu, Oezlem (Tit.-Prof.)
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08799 - Imamoglu, Oezlem (Tit.-Prof.)
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08799 - Imamoglu, Oezlem (Tit.-Prof.)
en_US
ethz.date.deposited
2021-03-09T08:04:09Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-03-24T10:21:52Z
ethz.rosetta.lastUpdated
2022-03-29T05:57:32Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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