Browsing University of Waterloo by Subject "Roth's theorem"
Now showing items 1-3 of 3
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A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression
(Springer, 2009-01-31)Let r1, . . . , rs be non-zero integers satisfying r1 + · · · + rs = 0. Let G Z/k1Z⊕· · ·⊕Z/knZ be a finite abelian group with ki |ki−1(2 ≤ i ≤ n), and suppose that (ri , k1) = 1(1 ≤ i ≤ s). Let Dr(G) denote the maximal ... -
A Prime Analogue of Roth's Theorem in Function Fields
(Springer New York, 2015)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 ... -
Roth's theorem on systems of linear forms in function fields
(Institute of Mathematics, 2010)1. Introduction. For r, s ∈ N = {1, 2, . . .} with s ≥ 2r + 1, let (bi,j ) be an r×s matrix whose elements are integers. Suppose that bi,1+· · ·+bi,s = 0 (1 ≤ i ≤ r). Suppose further that among the columns of the matrix, ...