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
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