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Proceedings of the London Mathematical Society Advance Access published online on March 28, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn013
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© 2008 London Mathematical Society

Simultaneous prime specializations of polynomials over finite fields

Paul Pollack

6188 Kemeny Hall
Mathematics Department
Dartmouth College
Hanover, NH 03755
USA

Received 11 July 2007. Revision received 17 January 2008.

Recently the author proposed a uniform analogue of the Bateman–Horn conjectures for polynomials with coefficients from a finite field (that is, for polynomials in Fq[T] rather than Z[T]). Here we use an explicit form of the Chebotarev density theorem over function fields to prove this conjecture in particular ranges of the parameters. We give some applications including the solution of a problem posed by Hall.

This research was conducted while the author was supported by an NSF Graduate Research Fellowship.

2000 Mathematics Subject Classification 11T55 (primary), 11N32 (secondary).


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