Phantom holomorphic projections arising from Sturm's formula

• Verfasst von: Maurischat, Kathrin [VerfasserIn]
• Verfasst von: Weissauer, Rainer [VerfasserIn]
• Titel: Phantom holomorphic projections arising from Sturm's formula
• Verf.angabe: Kathrin Maurischat, Rainer Weissauer
• Umfang: 26 S.
• Fussnoten: Gesehen am 12.02.2019
• Titel Quelle: Enthalten in: The Ramanujan journal
• Jahr Quelle: 2018
• Band/Heft Quelle: 47(2018), 1, S. 21-46
• ISSN Quelle: 1572-9303
• DOI: doi:10.1007/s11139-018-0033-8
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1587559285

Abstract

We construct Siegel Poincaré series of weight three and genus two outside their natural domain of convergency by the method of analytic continuation. In contrast to genus two Poincaré series of higher weights greater three, the Poincaré series thus obtained do not define holomorphic cuspforms of weight three. In fact, additional nonholomorphic phantom parts show up and we are able to describe them explicitly in terms of holomorphic forms of weight one. As a consequence of this result on Poincaré series, in the case under consideration we can also show that Sturm’s operator not only projects to the holomorphic discrete series of weight three, as one would expect, but also gives rise to an additional phantom projection.