000			nam a22 7a 4500
999			_c28894 _d28894
008			180212b xxu||||| |||| 00| 0 eng d
020			_a9781470425883
082			_a515.2433 _bTAO
100			_aTao, Terence
245			_aHigher order fourier analysis
260			_bRhode Island, _aAmerican Mathematical Society: _c2012
300			_ax, 187 p. _c24 cm.
365			_aINR _b990.00
440			_aGraduate studies in mathematics ; volume 142
520			_aTraditional Fourier analysis, which has been remarkably effective in many contexts, uses linear phase functions to study functions. Some questions, such as problems involving arithmetic progressions, naturally lead to the use of quadratic or higher order phases. Higher order Fourier analysis is a subject that has become very active only recently. Gowers, in groundbreaking work, developed many of the basic concepts of this theory in order to give a new, quantitative proof of Szemerédi's theorem on arithmetic progressions. However, there are also precursors to this theory in Weyl's classical theory of equidistribution, as well as in Furstenberg's structural theory of dynamical systems. This book, which is the first monograph in this area, aims to cover all of these topics in a unified manner, as well as to survey some of the most recent developments, such as the application of the theory to count linear patterns in primes. The book serves as an introduction to the field, giving the beginning graduate student in the subject a high-level overview of the field. The text focuses on the simplest illustrative examples of key results, serving as a companion to the existing literature on the subject. There are numerous exercises with which to test one's knowledge"
650			_aNumber theory
650			_aEstimates on exponential sums
650			_aFourier analysis
650			_aDynamical systems
650			_aErgodic theory
650			_aHarmonic analysis
942			_2ddc _cBK