Tsukuba Journal of Mathematics

On Doi-Naganuma lifting

Balesh Kumar and Murugesan Manickam

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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.

Article information

Source
Tsukuba J. Math., Volume 40, Number 2 (2016), 125-137.

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

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1492104600

Digital Object Identifier
doi:10.21099/tkbjm/1492104600

Mathematical Reviews number (MathSciNet)
MR3635382

Zentralblatt MATH identifier
06710501

Subjects
Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 11F32: Modular correspondences, etc.

Keywords
Doi-Naganuma lift Hilbert modular forms

Citation

Kumar, Balesh; Manickam, Murugesan. On Doi-Naganuma lifting. Tsukuba J. Math. 40 (2016), no. 2, 125--137. doi:10.21099/tkbjm/1492104600. https://projecteuclid.org/euclid.tkbjm/1492104600


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