Now showing items 1-5 of 5

• #### 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 generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression (II) ﻿

(Elsevier, 2011-02)
Let G ≃ Z/k1Z ⊕ · · · ⊕ Z/kN Z be a finite abelian group with ki |ki−1 (2 ≤ i ≤ N). For a matrix Y = (ai,j) ∈ Z R×S satisfying ai,1 + · · · + ai,S = 0 (1 ≤ i ≤ R), let DY (G) denote the maximal cardinality of a set ...
• #### A generalization of Roth's theorem in function fields ﻿

(World Scientific Publishing, 2009-11)
Let 𝔽q[t] denote the polynomial ring over the finite field 𝔽q, and let formula denote the subset of 𝔽q[t] containing all polynomials of degree strictly less than N. For non-zero elements r1, …, rs of 𝔽q satisfying r1 ...
• #### 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, ...

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