Nonvanishing of Koecher–Maass series attached to Siegel cusp forms

We prove a nonvanishing result for Koecher–Maass series attached to Siegel cusp forms of weight k and degree n in certain strips on the complex plane. When n=2, we prove such a result for forms orthogonal to the space of the Saito–Kurokawa lifts ‘up to finitely many exceptions’, in bounded regions....

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 281; pp. 624 - 669
Main Authors Das, Soumya, Kohnen, Winfried
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2015
Subjects
Koecher–Maass series
Siegel modular forms
secondary
Koecher–Maass series
Siegel modular forms
primary
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Summary:We prove a nonvanishing result for Koecher–Maass series attached to Siegel cusp forms of weight k and degree n in certain strips on the complex plane. When n=2, we prove such a result for forms orthogonal to the space of the Saito–Kurokawa lifts ‘up to finitely many exceptions’, in bounded regions.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2015.05.007