On the Doi-Naganuma lifting associated with imaginary quadratic fields

Tetsuya Asai
1978 Nagoya mathematical journal  
Similarly to the real quadratic field case by Doi and Naganuma ([3], [9]) there is a lifting from an elliptic modular form to an automorphic form onSL2(C) with respect to an arithmetic discrete subgroup relative to an imaginary quadratic field. This fact is contained in his general theory of Jacquet ([6]) as a special case. In this paper, we try to reproduce this lifting in its concrete form by using the theta function method developed first by Niwa ([10]); also Kudla ([7]) has treated the real
more » ... as treated the real quadratic field case on the same line. The theta function method will naturally lead to a theory of lifting to an orthogonal group of general signature (cf. Oda [11]), and the present note will give a prototype of non-holomorphic case.
doi:10.1017/s0027763000021693 fatcat:g2wvzpamtrainoeithvmu7hyou