Browsing University of Waterloo by Subject "function fields"
Now showing items 19 of 9

Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields
(University of Waterloo, 20100629)The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the HardyLittlewood circle method to investigate the density of rational ... 
Equidistribution of Polynomial Sequences in Function Fields, with Applications
(University of Waterloo, 2023)We provide a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greater than or equal to the characteristic ... 
Multidimensional Vinogradovtype Estimates in Function Fields
(Cambridge University Press, 2014)Let Fq[t] denote the polynomial ring over the finite field Fq. We employ Wooley’s new efficient congruencing method to prove certain multidimensional Vinogradovtype estimates in Fq[t]. These results allow us to apply a ... 
A note on character sums in finite fields
(Elsevier, 201707)We prove a character sum estimate in Fq[t] and answer a question of Shparlinski. 
On sets of polynomials whose difference set contains no squares
(Institute of Mathematics: Polish Academy of Sciences, 2013)Let Fq[t] be the polynomial ring over the finite field Fq, and let GN be the subset of Fq[t] containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set A⊆GN for which A−A ... 
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 nonzero 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, ... 
Some additive results in F_q[t]
(University of Waterloo, 20150827)We collected several results in integers of additive number theory and translated to results in F_q[t]. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, a ... 
The Unrestricted Variant of Waring's Problem in Function Fields
(Adam Mickiewicz University, 200709)Let J k q [t] denote the additive closure of the set of k th powers in the polynomial ring Fq[t], defined over the finite field Fq having q elements. We show that when s>k + 1 and q>k 2k+2 , then every polynomial in ...