Index

2-coboundary, 78

99% inverse theorem for the Gowers

norms, 75

W -trick, 124

δ-equidistribution, 12

additive cohomology, 77

additive quadruple, 83

algebraic set, 138

algebraic variety, 142

almost periodicity, 40

analytic rank, 72

arithmetic regularity lemma (strong),

38

arithmetic regularity lemma (weak), 38

asymptotic equidistribution, 3, 10

asymptotic notation, 3

asymptotic notation (ultralimit

analysis), 21

atom, 33

Balog-Szemer´edi-Gowers-Freiman

theorem, 84

Bezout’s theorem, 141

bias, 64

Bogdanov-Viola lemma, 66

Bohr set, 116

bounded (ultralimit analysis), 21

bracket polynomial, 102

Cauchy-Schwarz complexity, 55

Cauchy-Schwarz inequality, 149

Cauchy-Schwarz-Gowers inequality, 58,

157

characteristic, 55

Chevalley-Warning theorem, 63

classical polynomial, 61

cocycle, 77

complex conjugation, 151

complexity of a nilmanifold, 101

complexity of a nilsequence, 102

complexity of an algebraic set, 139

conditional expectation, 33

continuity of dimension, 140

continuity of irreducibility, 143

converse inverse theorem for the Gowers

norms, 75

correlation condition, 121

correspondence principle, 175

de Broglie’s law, 176

degree, 94

dense model theorem, 111, 121

density increment argument, 28

differentiation of nilsequences, 104

dimension, 140

Dirac measure, 3

energy increment argument, 33

equidistribution, 62

Equidistribution (abelian linear

sequences), 7

Equidistribution (abelian

multidimensional polynomial

sequences), 11

Equidistribution (abelian polynomial

sequences), 9, 17, 24

185