A Prime Analogue of Roth's Theorem in Function Fields
Abstract
Abstract. Let Fq[t] denote the polynomial ring over the nite eld Fq, and let PR denote the subset of
Fq[t] containing all monic irreducible polynomials of degree R. For non-zero elements r = (r1; r2; r3) of Fq
satisfying r1 + r2 + r3 = 0, let D(PR) = Dr(PR) denote the maximal cardinality of a set AR PR which
contains no non-trivial solution of r1x1 + r2x2 + r3x3 = 0 with xi 2 AR (1 i 3). By applying the
polynomial Hardy-Littlewood circle method, we prove that D(PR) q jPRj=(log log log log jPRj).
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Cite this version of the work
Yu-Ru Liu, Craig V. Spencer
(2015).
A Prime Analogue of Roth's Theorem in Function Fields. UWSpace.
http://hdl.handle.net/10012/20004
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