On the proof of the reciprocity law for arithmetic Siegel modular functions |
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Authors: | Walter L Baily |
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Institution: | (1) Department of Mathematics, The University of Chicago, 5734 University Avenue, 60637 Chicago, Illinois, USA |
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Abstract: | Earlier we obtained a new proof of Shimura’s reciprocity law for the special values of arithmetic Hilbert modular functions.
In this note we show how from this result one may derive Shimura’s reciprocity law for special values of arithmetic Siegel
modular functions. To achieve this we use Shimura’s classification of the special points of the Siegel space, Satake’s classification
of the equivariant holomorphic imbeddings of Hilbert-Siegel modular spaces into a larger Siegel space, and, finally, a corrected
version of some of Karel’s results giving an action of the Galois group Gal(Qab/Q) on arithmetic Siegel modular forms.
Research supported in part by the NSF Grant No. DMS-8601130. |
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Keywords: | Reciprocity law arithmetic Siegel modular functions Siegel space |
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