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Iwaniec H., Kowalski E. — Analytic number theory

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Название: Analytic number theory

Авторы: Iwaniec H., Kowalski E.

Аннотация:

This book shows the scope of analytic number theory both in classical and moderb direction. There are no division kines, in fact our intent is to demonstrate, partic ularly for newcomers, the fascinating countless interrelations.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 615

Добавлена в каталог: 01.04.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\ell$ -adic cohomology      269
$\ell$ -adic cohomology groups with compact support      304
$\ell$ -adic sheaf      310
$\Lambda^2$ -sieve      160 430
A-process      204 211 215
Abel — Jacobi theorem      299 543
Abelian variety      145 146
Absolute logarithmic height      541
Absolute values      541
Additive binary problem      468
Additive character      44 175 181 271 467 475
Additive function      9 28
Additive reduction      365
Adjoint square      137 373
Algebraic curves      145
Algebraic surface      310
Almost primes      159
Ambiguous classes      509
Ambiguous form      507
Amplification method      379 597
Amplifier      596
Analytic conductor      95
Analytic L-function      141 143 149
Approximate functional equation      97 257
Arithmetic etale fundamental group      300
Artin L-functions      96 126 141 356
Artin — Shreier covering      302
Automorphic form      61 93 131
Automorphic L-functions      84 93 375
Auxiliary polynomial      282
Averaging technique      357 387
B-process      204 211 216
Bad reduction      364
Bernoulli numbers      67
Bernoulli polynomial      66 484
Bessel function      72 73 90 91 245 258 358 386 408 411 454 512
Betti numbers      305 307
Bilinear form      169 174 186 218 326 340 343 346 350 420
Binary quadratic forms      498 503
Birch and Swinnerton — Dyer conjecture      148 367 520 538 578 579
Brun — Titchmarsh inequality      167 420
Buchstab identity      349
Burgess' bound      536
Canonical height      541
Cauchy's inequality      162 169 220
Central character      540
Central critical point      577
Central value      514 529
Character sum      74 101 365 422 429
Characters      43 487
Chebotarev density theorem      143 489
Circle method      171 315 443
Class group      58 510
Class group character      59 131 134 361 369 516
Class number      58 125 368 402 504 523 537 569
Class number formula      38 124 402 513 516
Class number one problem      124 577
Closed point      297
Cohen — Lenstra heuristics      510
Combinatorial sieve      164
Companion sums      273 278
Complete exponential sum      458
Complete family      573
Complete L-function      94
Complete sums      269 318
Completing technique      318
Complex multiplication      367 369
Conductor      45 60 93 94 109 130 149 190 247 365 539 572 579 597
Conductor exponent      365
Congruence subgroup      354
Conjugacy classes      394
Constant term in the Fourier expansion      390
Continuous spectrum      75
Converse theorems      377
Convexity bound      101 119 137 244 535 549 553 595
Critical line      113 547 562
Critical strip      96 101 105 113 145
Critical zero      547 563
Cubic Gauss sum      491
Cusp      355 387
Cusp form      61 65 83 136 186 356 368 479 574
Dedekind eta function      450 516 544
Dedekind multiplier system      450
Dedekind sum      450 456 516
Dedekind zeta function      125 513
Degree      94
Deligne bound      291 357 379 493 532
Density conjecture      232 249 265
Density theorem      420 547 596
Determinant equation      383
Deuring — Heilbronn phenomenon      428
Difference between consecutive primes      266
Differencing process      201 204 211 212 220 330 466
Diophantine approximation      282
Dirichlet approximation theorem      199 457
Dirichlet character      45 179
Dirichlet convolution      12 590
Dirichlet divisor problem      21 79 198 215
Dirichlet L-functions      45 83 84 182 267 324 329 368 388 479 513 534 573 579
Dirichlet polynomial      194 229 253 429 549 550 554
Dirichlet series      11
Discrete subgroup      354
Discrete valuation      292 301
Discriminant      363
Dispersion method      171
Divisor function      13 74 86 334
Divisor on a curve      293
Dual sum      170 468
Duality principle      170 174 184 189 234
Effective divisor      293 298
Eichler — Shimura theory      367
Eisenstein series      80 357 360 369 388 411 479 491 511 588
Elliptic curve      145 190 269 313 363 403 520 529 574
Elliptic differential operator      386
Elliptic functions      543
Elliptic motion      395
Epstein zeta function      513
Equidistribution      130 137 198 313 352 487
Etale covering      300
Euler characteristic      307
Euler Idoneal Number Problem      520
Euler Pentagonal Numbers Theorem      449 456
Euler product      11 41 45 60 94 113 146 297 366 371 493 521 529 551 564
Euler — Maclaurin formula      66 68 76 206 483 485
Exceptional character      37 434
Exceptional eigenvalues      390 399 410 497
Exceptional zero      93 111 112 121 140 390 428 434
Exceptional zero repulsion      428
Exclusion-inclusion      145 156 171 308 339
Explicit formula      108 118 127 265 337 410 440 564
Exponent pair      214
Exponent Pair Hypothesis      86 214
Exponential integrals      206 208
Exponential sums      197 225 443 456
Family of exponential sums      312
Family of L-functions      96 175 573 580
Farey sequence      451 458 469 477
Ford circle      452
Four squares theorem      468
Fourier coefficients      174
Fourier coefficients of cusp forms      319 404
Fourier coefficients of modular forms      83 291 479
Fourier expansion at infinity      132
Fourier integrals      204
Fricke involution      83 366 368
Frobenius automorphism      270 302
Frobenius conjugacy class      302
Function field      292 301
Functional equation      81 84 94 244 258 362 366 368 375 377 512 530 539 547 566 582
Functional equation of Eisenstein series      389

functor      301
Fundamental discriminant      52 124 508 538 540 543
Fundamental domain      58 354 396 499 504 521
Fundamental lemma      153 159 437
Fundamental unit      38 402 516
Gamma factor      94
Gauss circle problem      20 73 198 215
Gauss sum      18 47 49 60 79 84 119 179 192 199 239 274 321 347 456 474 478 488 491 495
Gauss — Bonnet formula      355
Gaussian prime      53 130 290
Gaussian unitary ensemble      563 570
Genus character      362 516
Genus theory      480 506 540
Geometric Frobenius      302 304
Geometric fundamental group      304
Goldbach problem      171 339
Good reduction      364
Grand Density Conjecture      250
Grand Riemann hypothesis      101 113 136 175 182 194 249 324 419 577
GRH      113
Gross — Zagier curve      368
Gross — Zagier formula      579
Group law on elliptic curves      291
Haar measure      487
Hadamard and de la Vallee Poussin      41 101 306
Hankel transform      71 99
Harish-Chandra/Selberg transform      393 397 501
Harmonic polynomial      362
Harmonics      9 174 239 319 356 360 383
Hasse bound      193 269
Hasse derivative      282
Hasse — Weil zeta function      99 145 146 272 366 369 539 541 579
Hecke basis      574
Hecke character      56 59 129 141 142 302 362
Hecke congruence groups      354
Hecke eigenvalues      134 192 513 582
Hecke form      372
Hecke L-function      60 86 366 368 374 379 511 574
Hecke operator      80 186 367
Heegner point      494 542—544 579
Heilbronn sums      300
Higher von Mangoldt function      16 592
Hilbert class field      544
Hilbert inequality      175
Hilbert's theorem      90 296
Hybrid large sieve      183
Hyperbola method      22 31 37 420
Hyperbolic conjugacy classes      401
Hyperbolic geodesics      384
Hyperbolic Laplacian      385
Hyperbolic measure      354 514
Hyperbolic motion      395
Hyperbolic plane      384
Hyperelliptic curve      281 287
Idoneal number      508
Imaginary quadratic field      17 56 361 503 508 542
Incomplete character sum      317
Incomplete Eisenstein series      387 389
Incomplete gamma function      513
Incomplete Kloosterman sum      471
Invariant integral operator      392 393
Isoperimetric inequality      398
J-invariant      364
Jacobi inversion formula      473
Jacobi sum      49 311 491
Jacobi symbol      52 473
Jacobian variety      147 578
Kloosterman fractions      185 481
Kloosterman sum      18 78 185 187 278 308 313 322 382 404 469 476 481 492 584
Kloosterman sums zeta-function      412
Kloosterman zeta function      278
Kloosterman — Salie sum      281 358
Kronecker limit formula      516 524
Kronecker symbol      52 57 124 506 508 530
Kuznetsov formula      65 186 380
L-functions of varieties      96
Langlands Functoriality      96 369 493
Langlands program      132
Laplace operator      89 131 132 186 362 404 563 580
Large sieve      164 167 174 194 239 420 595
Large sieve inequality      125 423 580
Lattice points      197
Least quadratic non-residue      182
Lefschetz trace formula      305 310
Legendre formula      155 341
Legendre symbol      271
Length of closed geodesics      410
Length spectrum      401
Levinson's method      550
Lindeloef hypothesis      101 116 186 194 214 235 243 256 597
Linear equivalence classes      298
Linear forms      497 499
Linear fractional transformation      353 504
Linearly equivalent divisors      293
Liouville function      14
Lisse $\ell$ -adic sheaf      301
Local Langlands conjecture      138
Local root number      136
Local roots      94
Local zeta function      365
Log-free zero-density estimate      428
Low-lying zero      574
Maass form      131 387
Major arc      467
Matrix coefficients      487
Mellin transform      61 90 257
Mertens formula      34
Minimal model      364
Minor arc      457 462 464 466 467
Mixed of weights $\leq \omega$       305
Mobius function      32 36 42 345 421 430 443 446 590
Mobius inversion      13 44 46 154
Mobius Randomness Law      338 444
Modular curves      577
Modular form      145 356
Modular form of weight one      356
Modular group      503
Modular interpretation      542
Modular parameterization      542 543 545
Modularity conjecture      191 366
Mollification      550 562 581
Mollifier      251
Monodromy group      313 573
Mordell — Weil theorem      579
Multiple Kloosterman sum      308 492
Multiplicative characters      34 271 308
Multiplicative function      154 165 339 521
Multiplicative inverse      19 55
Multiplicative reduction      365
Multiplicity one principle      373
Near-orthogonality      170 192
Nebentypus      131
Negative curvature      384
Newton polyhedron      308 309
Norm map      270
Numerus idoneus      508
Order of vanishing of an L-function      117
Orthogonality of characters      35 46 121 311 318 425 482 492
Orthogonality relations      44 45 179 271 511
Pair correlation conjecture      266 569
Parabolic motion      395
Peter — Weyl theorem      487
Petersson formula      136 187 188 380 404 411 579 580
Petersson inner product      357 371
Petersson norm      138 542 595
Poincare duality      305
Poincare metric      353 384
Poincare series      357 404 500
Poincare upper half-plane      353 384
Point-pair invariant      391

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