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December 2016 On Doi-Naganuma lifting
Balesh Kumar, Murugesan Manickam
Tsukuba J. Math. 40(2): 125-137 (December 2016). DOI: 10.21099/tkbjm/1492104600

Abstract

In this paper, we extend the Doi-Naganuma lifting as suggested by Kudla [4], on the lines of Zagier's work [6]. For each fundamental discriminant D associated with a real quadratic field, we prove that there exists a Hecke-equivarient map ιD which maps the mth Poincare series of weight k, level M and character χD = (./D) into a Hilbert cusp form of weight k, level M/D associated with the real quadratic field of discriminant D of class number one. Through this, we get its adjoint ι*D with respect to the Petersson inner product.

Citation

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Balesh Kumar. Murugesan Manickam. "On Doi-Naganuma lifting." Tsukuba J. Math. 40 (2) 125 - 137, December 2016. https://doi.org/10.21099/tkbjm/1492104600

Information

Received: 24 March 2016; Revised: 8 September 2016; Published: December 2016
First available in Project Euclid: 13 April 2017

zbMATH: 06710501
MathSciNet: MR3635382
Digital Object Identifier: 10.21099/tkbjm/1492104600

Subjects:
Primary: 11F32, 11F41

Rights: Copyright © 2016 University of Tsukuba, Institute of Mathematics

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Vol.40 • No. 2 • December 2016
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