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The Kubota symbol for Sp(4, Q(i))1)

Published online by Cambridge University Press:  22 January 2016

Daniel Bump ,
Solomon Friedberg  and
Jeffrey Hoffstein
Daniel Bump
Affiliation:
Department of Mathematics Stanford University, Stanford, CA 94305, U.S.A.
Solomon Friedberg
Affiliation:
Department of Mathematics The University of California at Santa Cruz, Santa Cruz, CA 95064, U.S.A.
Jeffrey Hoffstein
Affiliation:
Department of Mathematics Brown University, Providence, RI 02912, U.S.A.
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Following eariler work of Kubota and Mennicke, the major work of Bass, Milnor and Serre [1] constructed characters of congruence subgroups of the modular subgroups of SL(n) and Sp(2n) over a totally complex number field, which are related to the power residue symbol. They do not obtain the lowest possible level of these Kubota characters, nor does it appear possible to modify their arguments to extend the characters to the lowest possible level.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 119 , September 1990 , pp. 173 - 188
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

Footnotes

1)

This work was supported by grants from the NSF.

References

[1] Bass, H., Milnor, J. and Serre, J.-P., Solution of the congruence subgroup problem for SLn (n≥3) and Sp2n (n≥2)., Publ. Math. IHES, 33 (1967), 59–137.CrossRefGoogle Scholar
[2] Bump, D., Friedberg, S. and Hoffstein, J., Eisenstein series on the metaplectic group and non vanishing theorems for automorphic L-functions and their derivatives, Ann. of Math., 131 (1990), 53–127.CrossRefGoogle Scholar
[3] Johnson, D. and Millson, J., Modular Lagrangians and the theta multiplier, Preprint (1988).Google Scholar
[4] Stark, H., On the transformation formula for the symplectic theta function and applications, J. Fac. Sci. Univ. Tokyo, 29 (1982), 1–12.Google Scholar
[5] Styer, R., Prime determinant matrices and the symplectic theta function, Amer. J. Math., 106 (1984), 645–664.CrossRefGoogle Scholar