Granville A. (ed.), Rudnick Z. (ed.) — Equidistribution in Number Theory, an Introduction :: Электронная библиотека попечительского совета мехмата МГУ

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Granville A. (ed.), Rudnick Z. (ed.) — Equidistribution in Number Theory, an Introduction

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Название: Equidistribution in Number Theory, an Introduction

Авторы: Granville A. (ed.), Rudnick Z. (ed.)

Аннотация:

Written for graduate students and researchers alike, this set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos.

The volume brings together leading researchers from a range of fields, whose accessible presentations reveal fascinating links between seemingly disparate areas.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 345

Добавлена в каталог: 12.03.2008

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Предметный указатель

3-term arithmetic progression      9
Additive function      23
Adelic point      161
Andre — Oort conjecture      114 120 121 126 134
Anticanonical height      169 175
Arithmetic QUE      340
Bilu equidistribution theorem      98
Bit generator      40 41
Blowing up      170 171 181 191
Bogomolov conjecture      117—119
Brauer — Manin obstruction      161 162 165
Burgess’s bound      212
Canonical commutation relations      333
Capacity      100
Carmichael function      41—43
Cat map      333
Cayley cubic      172 173 190
Central limit theorem      16 21
Chebyshev’s bias      73
CM point      103 104 114 124—126 133 134 199
Communication complexity      48 49
Complementary series      251
Coprimality conditions      175 179—181 183 184 186
Cramer’s model      60
Cryptography      32 37
Cuspidal      254
Cycling attack      44
Del Pezzo surface      169 171 175 177 178 189 191
Del Pezzo surface, singular      171
Del Pezzo surface, smooth      170 172 195
Diffie — Hellman key exchange      32
Discrepancy      30 31 35 46 47 49
Discrete logarithm      32 33
Discrete series      251
Distribution of reduced residues      72
Division point      85
Egorov’s theorem      333 338
Eisenstein series      255
Elliptic curve      5 85
Energy      96
entropy      281
Equidistribution      103 104 107 114 117—119 126 130 132 133
Equidistribution conjecture      116 125 131 132
Equidistribution, quantum      305
Equilibrium measure      97
Equivariant compactification      177 178
Erdos — Kac theorem      17
Ergodic      264 316
Exceptional curve      181
Exponential sums      29—32 46 50 55
Fano varieties      170 172
Fourier transform      8
Gauss formula      210
Gauss sum      56
Hardy — Littlewood conjecture      61
Harmonic polynomial      202
Hecke correspondence      109 122 278 297
Hecke operator      109 110 112 256 278 279 297 340
Hecke point      103 104 109
Hecke’s bound      201
Height      103 107 119
Higher moments of primes in intervals      70
Homogeneous space      245
Intersection number      170 171
Iwaniec estimate      209
Jacobi theta series      200
Kloosterman sum      205
Kubilius — Shapiro theorem      25
Lang’s conjecture      86
lattice points in a right-angled triangle      1
Lehmer’s conjecture      100
Linnrk      197
Littlewood’s conjecture      263 288
Local densities      154
Mahler measure      94
Mahler’s compactness criterion      290
Maier’s matrix method      75

major arcs      143 146 147 149 159 163
Manin — Mumford conjecture      86 114 118—120
Manin’s conjecture      169 171 172 174—178 190
Mechanics, classical      306
Mechanics, quantum      319
Minimal desingularization      171 177
Minor arcs      143 146 159 163
Mixing      253 264 318
Mordell’s conjecture      86
Neron — Severi torus      174
Norm from      161
Normal distribution      16
Normal numbers      11
Normal order      15
Number of distinct prime factors      15
Oppenheim conjecture      262 273
Orbit, periodic      270
Pair correlation      70
Periodic      270
Picard group      170 171 174
Poincare series      204
Poisson distribution of primes      60
Polynomial time      32
Potential function      101
Power generator      38—41 44 46 50
Prime number theorem      59
Primitive root      32 52
Principal series      251
pseudorandom      29 37 38
Quantum chaos      305
Quantum equidistribution      305
Quantum ergodicity      337
Quantum unique ergodicity      295 339
Quantum unique ergodicity, arithmetic      340
Rankin — Selberg method      206
Ratner’s theorems      269
RSA cryptosystem      44
Scars      340
Schnirelman theorem      328
Semi-classical analysis      322 325
Shimura lift      203
Shimura varieties      103 104 114 120 125 126 134 135
Siegel’s theorem      210
Sieve theory      20
Singular integral      150
Singular moduli      212
Singular series      61 153 154
Small height      98
Special point      114—116 121 123 124
Specoal point      114
Spectral decomposition      104 110—113 247
Spectral theorem      249 251
Split      172
Stone — von Neuman theorem      333
Strict      98
Subconvexity      212
Timed-release crypto      45
Topological entropy      285
Toral automorphisms      305
Torsion point      85 114 117—119
Torsion subvariety      98
Torsor equations      175
Trace formula      258
Uncertainty principle      79
Uniform distribution      29—31 35 39 40
Uniformly distributed mod one      2 5
Unipotent      269
Uniquely ergodic      265
Universal torsor      174—176 179 180 189—192 194 195
Vanishing sums of roots of unity      88
Variance of primes in intervals      68
Variational Principle      285
Weyl      157
Weyl criterion      3 30 31 33 34 37
Weyl quantization      332
Weyl sum      202
Zhang’s theorem      99

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