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On the imaginary quadratic Doi-Naganuma lifting of modular forms of arbitrary level

Published online by Cambridge University Press:  22 January 2016

Solomon Friedberg
Solomon Friedberg*
Affiliation:
Department of Mathematics, Harvard University, Science Center, One Oxford Street, Cambridge, Massachusetts 02138, USA
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In this paper, we use the theta function method [10] to give explicit Doi-Naganuma type maps associated to an imaginary quadratic field K, lifting cusp forms on any congruence subgroup of SL(2, Z) to forms on SL(2, C) automorphic with respect to an appropriate arithmetic discrete subgroup. The case of class number one, and form modular with respect to group Γ0(D) and character χ0 = (–D/*), where –D is the discriminant of K has been treated by Asai [1]. In order to complete his discussion, we must first introduce a more general theta function associated to an indefinite quadratic form (here of type (3, 1)), which we regard as a specialization of a symplectic theta function (see also [4]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 92 , December 1983 , pp. 1 - 20
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

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