• On the proof of the reciprocity law for arithmetic Siegel modular functions

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      https://www.ias.ac.in/article/fulltext/pmsc/097/01-03/0021-0030

    • Keywords

       

      Reciprocity law; arithmetic Siegel modular functions; Siegel space

    • 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.

    • Author Affiliations

       

      Walter L Baily1

      1. Department of Mathematics, The University of Chicago, 5734 University Avenue, Chicago, Illinois - 60637, USA
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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