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Vanishing sums in function fields

Published online by Cambridge University Press:  24 October 2008

W. D. Brownawell  and
D. W. Masser
W. D. Brownawell
Affiliation:
Department of Mathematics, Pennsylvania State University, State College, PA 16802, U.S.A.
D. W. Masser
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.
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Extract

Let k be a field of zero characteristic, and let F be a function field over k of genus g. We normalize each valuation v on F so that its order group consists of all rational integers, and for elements u1, …, un of F, not all zero, we define the (projective) height as

The sum formula on F shows that this is really a height on the projective space .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 427 - 434
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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