Iwaniec H., Kowalski E. — Analytic number theory :: Электронная библиотека попечительского совета мехмата МГУ

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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

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 615

Добавлена в каталог: 01.04.2006

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

Предметный указатель

Poisson distribution      266
Poisson summation formula      61 69 75 99 204 319 359 391 398 404 473
Polya — Vinogradov inequality      325 326 523 524
Positivity      41 105 157 180 377
Primary element      54
Prime number theorem      25 31 110 264 401 419 427 446 448 489 527 567
Primes in arithmetic progressions to large moduli      266
Primes in short intervals      264 266
Primes splitting completely      521
Primitive character      46 48 70 79 85 119 179 244 422 491 508 597
Primitive conjugacy classes      396 402
Primitive cusp form      99 134 370 373 374 513 529
Primitive Hecke character      60
Primitive ideal      57 508
Primitive root      271
Principal divisors      293
Principal genus      506
Pure of weight $\omega$       305
Quadratic character      184
Quadratic reciprocity law      51
Quantum unique ergodicity conjecture      494
Radius of convergence      289
Ramanujan $\Delta$ function      360 367 493 516
Ramanujan $\tau$ function      372
Ramanujan sum      18 44 48 179 280 323 325 461 472 478 481 483 488 587 589
Ramanujan — Petersson conjecture      95 100 101 115 131 137 146 378 391 480
Random matrix theory      563
Rankin — Selberg convolution      14 97 106 110
Rankin — Selberg L-function      97 118 189 375 378 535 580
Rankin's trick      341 349 525
Real character      46 49
Real primitive character      38 46 57 84 122 573 577
Real quadratic field      38 516
Reflection method      243 257
Regular discriminants      510
Regulator      125
Residual spectrum      388
Resolvent of the laplacian      390 405
Riemann hypothesis      305 306 309 320 337 427 514 518 524 547 563 568
Riemann hypothesis for curves over finite fields      146 329 463
Riemann Hypothesis for Dirichlet L-functions      443
Riemann Hypothesis for elliptic curves over finite fields      366
Riemann zeta function      12 119 197 204 216 388 561
Riemann — Roch theorem      294 296 298
Root number      94 142 145 367 377 538 574
Roots of an exponential sum      274
Roots of quadratic congruences      55
Salie sum      272 323 476 477 495
Sato — Tate conjecture      137 289 324 493
Sato — Tate measure      492
Scaling matrix      355 387
Scattering matrix      388 397
Selberg Eigenvalue Conjecture      96 390 415
Selberg sieve      160
Selberg trace formula      65 391
Self-dual L-function      95 106 578

Semistable      365
Separation of variables      326 350
Series of Kloosterman sums      380
Shifted primes      30 153
Short character sums      289 326
Siegel mass formula      481
Siegel — Walfisz theorem      419 427 489
Siegel's bound      124 479 514
Sieve dimension      157
Sieve methods      25 153 171 265 340 349 430 493
Sieve problem      27
Sieve weights      338
Sieving level      349
Sifted sum      153
Sifting range      161
Sign of the functional equation      95 537
Singular integral      460
Singular series      460 466 478
Smoothing      40 73 74 111 169 239 497
Special value      194 577 595
Spectral decomposition      403 406 501
Spectral theory      19 344
Spectral theory of Kloosterman sums      403
Square root cancellation      306 312 314
Strict divisor function      342
Strong multiplicity one principle      139 375
Subconvexity bound      101 204 329 494 554 597
Subdivision method      236
Sums of Kloosterman sums      410 586
Symmetric square      14 137 189 532 535 575 595
Tate twists      301
Tate — Shafarevitch group      367
Tempered divisor function      75
Theta function      18 61 85 361 456 473 479 513 541
Theta multiplier      186
Trace map      270
Trivial sheaf      306
Trivial zeros      96
Twisted modular form      133
Uncertainty principle      564
Unramified      94 118
Upper-bound sieve      430
von Mangoldt function      15 31 42
Voronoi formula      398
Waring problem      456
Weierstrass equation      363 543
Weil bound      79 130 269 288 381 403 413 472 585
Weil Conjectures      378
Well-factorable function      420
Well-spaced      175 218 232
Weyl Law      186 391
Weyl shift      216 314
Weyl sum      198 201 335
Zero-density theorem      249 264
Zero-detecting polynomials      252
Zero-free region      105 110 128 135 138 249 264 336 347 428 429
Zeta function of an exponential sum      273

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