Duke Mathematical Journal

Pullback of the lifting of elliptic cusp forms and Miyawaki's conjecture

Tamotsu Ikeda

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Abstract

We construct a lifting from Siegel cusp forms of degree r to Siegel cusp forms of degree r+2n. For r=n=1, our result is a partial solution of a conjecture made by Miyawaki [27, page 307] in 1992. In particular, we can calculate the standard L-function of a cusp form of degree 3 and weight 12, which is in accordance with Miyawaki's conjecture. We give a conjecture on the Petersson inner product of the lifting in terms of certain L-values

Article information

Source
Duke Math. J., Volume 131, Number 3 (2006), 469-497.

Dates
First available in Project Euclid: 6 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1139232347

Digital Object Identifier
doi:10.1215/S0012-7094-06-13133-2

Mathematical Reviews number (MathSciNet)
MR2219248

Zentralblatt MATH identifier
1112.11022

Subjects
Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Citation

Ikeda, Tamotsu. Pullback of the lifting of elliptic cusp forms and Miyawaki's conjecture. Duke Math. J. 131 (2006), no. 3, 469--497. doi:10.1215/S0012-7094-06-13133-2. https://projecteuclid.org/euclid.dmj/1139232347


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