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On the Doi-Naganuma lifting associated with imaginary quadratic fields

Published online by Cambridge University Press:  22 January 2016

Tetsuya Asai
Tetsuya Asai*
Affiliation:
Department of Mathematics, Faculty of General Education Ehime University
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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 on SL2(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 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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 71 , November 1978 , pp. 149 - 167
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

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