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September 2015 Saito–Kurokawa lifts of square-free level
Mahesh Agarwal, Jim Brown
Kyoto J. Math. 55(3): 641-662 (September 2015). DOI: 10.1215/21562261-3089127

Abstract

Let fS2κ2(Γ0(M)) be a Hecke eigenform with κ2 even and M1 and odd and square-free. In this paper we survey the construction of the Saito–Kurokawa lifting from the classical point of view. We also provide some arithmetic results on the Fourier coefficients of Saito–Kurokawa liftings. We then calculate the norm of the Saito–Kurokawa lift.

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Mahesh Agarwal. Jim Brown. "Saito–Kurokawa lifts of square-free level." Kyoto J. Math. 55 (3) 641 - 662, September 2015. https://doi.org/10.1215/21562261-3089127

Information

Received: 21 April 2014; Revised: 24 June 2014; Accepted: 25 August 2014; Published: September 2015
First available in Project Euclid: 9 September 2015

zbMATH: 1326.11019
MathSciNet: MR3395984
Digital Object Identifier: 10.1215/21562261-3089127

Subjects:
Primary: 11F32 , 11F46
Secondary: 11F66 , 11F67

Keywords: Bloch–Kato conjecture , congruences among automorphic forms , Galois representations , Saito–Kurokawa correspondence , Siegel modular forms , special values of $L$-functions

Rights: Copyright © 2015 Kyoto University

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Vol.55 • No. 3 • September 2015
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