Tsukuba Journal of Mathematics

On Doi-Naganuma lifting

Balesh Kumar and Murugesan Manickam

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.

Doi-Naganuma lift Hilbert modular forms


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

Export citation