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Bulletin of the London Mathematical Society Advance Access originally published online on February 25, 2009
Bulletin of the London Mathematical Society 2009 41(2):341-353; doi:10.1112/blms/bdp008
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© 2009 London Mathematical Society

Diophantine inequalities in function fields

Craig V. Spencer

School of Mathematics
Institute for Advanced Study
1 Einstein Drive
Princeton, NJ 08540
USA

Received 8 April 2008. Revision received 3 November 2008.

This paper develops the Bentkus–Götze–Freeman variant of the Davenport–Heilbronn method for function fields in order to count Fq[t]-solutions to diagonal Diophantine inequalities in Fq ((1/t)).

2000 Mathematics Subject Classification 11D75 (primary), 11P55, 11T55 (secondary).

This research was supported in part by NSF grants DMS-0601367 and DMS-0635607.


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