Tsukuba Journal of Mathematics
- Tsukuba J. Math.
- Volume 40, Number 2 (2016), 125-137.
On Doi-Naganuma lifting
In this paper, we extend the Doi-Naganuma lifting as suggested by Kudla , on the lines of Zagier's work . 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.
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
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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.
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