Patterson S.J. — An Introduction to the Theory of the Riemann Zeta-Function :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Patterson S.J. — An Introduction to the Theory of the Riemann Zeta-Function

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: An Introduction to the Theory of the Riemann Zeta-Function

Автор: Patterson S.J.

Аннотация:

This is a modern introduction to the analytic techniques used in the investigation of zeta-function. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory. Since then, many other classes of "zeta-function" have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasized central ideas of broad application, avoiding technical results and the customary function-theoretic approach.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 172

Добавлена в каталог: 28.10.2010

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

Предметный указатель

Algebraic geometry      76 82—84
Apery, R.      3
Approximate functional equation      8 23 50 67 91ff
Artin L-functions      82
Artin, E.      75
Bernoulli numbers      3
Beta function (B)      130
Cauchy, A.L.      4
Chebychev, P.      6 7
Cohomology theory      83
Computations      56—57 74
Convolution      118 123
Critical line      22 67
Curve Jacobian of      83—85
Curve over a finite field      75ff
Curve place of      76—78
Curve point of      78
Davenport, H.      56
Dirichlet integral      113
Dirichlet, P.G.L.      2 30 113 115
Distributions      18
Divisor functions $(d_{k}, \sigma_{t})$       9—10 31—32
Eisenstein, G.      12
Euclid      2
Euler constant $(\gamma)$       3 34 131—132
Euler function $(\varphi)$       9
Euler product      1—2 33 35 38—39 86—87
Euler, L.      1—4
Explicit formulae of prime number theory      6 38—39 43 44 79—80 85
Ferrar, W.      25
Finite field      76
Fourier integral      117
Fourier series      115 116
Fourier transform      116 117
Frobenius map      82 83
Function field      76
Gamma function $(\Gamma)$       4 130ff
Gamma function, product representation      131
Gauss, C.F.      6 7
Grothendieck, A.      83
Hadamard product      31—35
Hadamard, J.      7 31 50 90 141
Hardy, G.H.      8 75
Hasse, H.      76
Heath-Brown, D.R.      64 110
Integral function      138—139
Integral function, order of      139
Integral means of the zeta-function      59—64 68—69 97
Iwasawa theory      4 58
Legendre — Jacobi symbol      109
Legendre, A.M.      7
Lindeloef hypothesis      67—72
Littlewood, J.E.      8 59—60
Local functional equation      18
Logarithmic integral (Li)      6

Matsumoto, H.      86
Maximum principle, extended      142
Mellin transform      6 15 122ff
Moebius function $(\mu)$       9 49
Multi-set      33
Numbers, l-adic      83
Partial summation      53
Perron’s formula      44 123
Prime numbers      1 2 5—9 38 44 51—53 72—75
Ramanujan, S.      49
Riemann hypothesis      5 7 67 70 72—76 80—82 86—87
Riemann Hypothesis, Weil’s criterion      80—82
Riemann — Lebesgue lemma      111
Riemann — Siegel formula      91
Riemann, B.      4—9 22 55 91
Schmidt, F.K.      76
Selberg trace formula      79 137
Selberg, A.      22 48 79
Set with multiplications      33
Siegel, C.L.      8 9 91
Stepanov, S.A.      76
Stirling’s formula      22 133 134
Summation formula, Euler — Maclaurin      30
Summation formula, Poisson      14 25—26 108 118—119
Summation Formula, Voronoi      14 25 32
Tate’s thesis      18
Theorems, Backlund      149—151
Theorems, Bohr — Landau      59
Theorems, Davenport — Hasse      89
Theorems, Hadamard’s "Three Circles"      71 143
Theorems, Hardy — Selberg      75
Theorems, Jensen      70 138
Theorems, Littlewood      60 148
Theorems, Phragmen — Lindeloef      23 68 143 144
Theorems, Plancherel      117
Theorems, Prime Number      6 7 51—53
Theorems, Riemann Mapping      144
Theorems, Riemann — Roch      79
Theorems, Wiener — Ikehara      51
Type of a function      15 122
v. Mangoldt function (A)      9
v. Mangoldt, H.      7 55
v.d. Corput, J.G.      100
Variation      111—113
Variation, function of bounded      111
Variation, function of total bounded      111
Vinogradov, I.M.      8 65
Weierstrass, K.      141
Weil, A.      76 78 80 82 84
Weyl, H.      102
Zero set of Riemann zeta-functic      5 33 50
Zeta-function of curve over a finite field      78
Zeta-function, functional equation      4 19
Zeta-function, integral representation      17 23
Zeta-function, p-adic      4 85
Zeta-function, Riemann $(\xi)$       1ff

О проекте