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Some Remarks on Eisenstein Series for Metaplectic Coverings

Published online by Cambridge University Press:  20 November 2018

Lawrence Morris
Lawrence Morris*
Affiliation:
Clark University, Worcester, Massachusetts
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In recent years the harmonic analysis of n-fold (n > 2) metaplectic coverings of GL2 has played an increasingly important role in certain aspects of algebraic number theory. In large part this has been inspired by the pioneering work of Kubota (see [3] for example); as an application one could cite the solution by Heath-Brown and Patterson [3] to a question of Kummer's on the distribution of the arguments of cubic Gauss sums. In that paper, Eisenstein series on the 3-fold metaplectic cover of GL2(A) play a crucial role.

The object of this note is to point out that the theory of Eisenstein series can be made to work for a wide class of finite central coverings. Indeed, once the assumptions are made, the usual theory carries over readily, and one obtains a spectral decomposition of the appropriate L2-space of functions; this is done in Section 2 of this paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 6 , 01 December 1983 , pp. 974 - 985
Copyright
Copyright © Canadian Mathematical Society 1983

References

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