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Tori in metaplectic covers of GL2 and applications to a formula of Loxton–Matthews

Published online by Cambridge University Press:  24 October 2008

S. J. Patterson
S. J. Patterson
Affiliation:
Mathematisches Institut, Universität Göttingen, D-3400 Göttingen, West Germany
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Extract

In this paper we have two objectives. The first is to investigate the restriction of a metaplectic cover to an arbitrary torus in GL2. This will be explained at greater length below, and the main results are Theorems 1 and 2. The second is an application of the same ideas to introduce the arithmetic function P, which has already appeared in a special case in [9], and to prove the fundamental property given by Theorem 3. These theorems will be proved in §§ 2 and 3. In §§ 4 and 5 we remark on the appearence of the function P in the formula of Loxton and Matthews [5], [6] for the biquadratic Gauss sum and discuss the structure of this formula.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 2 , September 1986 , pp. 249 - 263
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

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