publication . Thesis . Other literature type . 2011

Topics in arithmetic combinatorics

Sanders, Tom;
English
  • Published: 27 Apr 2011
  • Publisher: University of Cambridge
  • Country: United Kingdom
Abstract
E-thesis pagination differs from approved hard bound copy, Cambridge University Library classmark: PhD.30726 This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1-norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these problems are, in some sense, qualitative or at the very least infinitary and it has become increasingly apparent that a quantitative state of affairs is desirable. Broadly speaking, the first part of the thesis develops three new tools for tackling the problems above: We prove a new structural theorem for the spectrum of functions in A(G); ...
Subjects
free text keywords: Fourier analysis, Freiman's theorem, Chang's theorem, Additive combinatorics, Littlewood's conjecture, Arithmetic combinatorics, Bourgain systems, Idempotent theorem, Local Fourier analysis, Induction on doubling, Discrete analysis
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publication . Thesis . Other literature type . 2011

Topics in arithmetic combinatorics

Sanders, Tom;