11 citations · 35 across the 7 of their papers we have counts for
8 papers
New quantitative estimates on the incidence geometry and growth of finite sets
Timothy G. F. Jones
This thesis establishes new quantitative records in several problems of incidence geometry and growth. After the necessary background in Chapters 1, 2 and 3, the following results…
A sum-product theorem in function fields
Thomas Bloom, Timothy G. F. Jones
Let be a finite subset of $\ffield$, the field of Laurent series in over a finite field . We show that for any there exists a constant dependent o…
Further improvements to incidence and Beck-type bounds over prime finite fields
Timothy G. F. Jones
We establish improved finite field Szemeredi-Trotter and Beck type theorems. First we show that if P and L are a set of points and lines respectively in the plane F_p^2, with |P|,|…
Improved bounds on the set A(A+1)
Timothy G. F. Jones, Oliver Roche-Newton
For a subset A of a field F, write A(A + 1) for the set {a(b + 1):a,b\in A}. We establish new estimates on the size of A(A+1) in the case where F is either a finite field of prime…
New results for the growth of sets of real numbers
Timothy G. F. Jones
We use the theory of cross ratios to construct a real-valued function f of only three variables with the property that for any finite set A of reals, the set f(A) = {f(a,b,c):a,b,c…
An improved incidence bound over fields of prime order
Timothy G. F. Jones
Let P be a set of points and a set of lines in (F_p)^2, with |P|,|L|\leq N and N<p. We show that P and L generate no more than C N^(3/2 - 1/806 + o(1)) incidences for some abso…