Koblitz N. — P-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd ed. (Graduate Texts in Mathematics) :: Электронная библиотека попечительского совета мехмата МГУ

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Koblitz N. — P-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd ed. (Graduate Texts in Mathematics)

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Название: P-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd ed. (Graduate Texts in Mathematics)

Автор: Koblitz N.

Аннотация:

The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.
Read more at http://ebookee.org/P-adic-Numbers-p-adic-Analysis-and-Zeta-Functions-Graduate-Texts-in-Mathematics-v-58_1258363.html#jv5KSgsWuzjvwkJS.99

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 1984

Количество страниц: 168

Добавлена в каталог: 18.04.2014

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Предметный указатель

$ord_{p}$ (p-adic ordinal)      2 66 72
$\Omega$ (completion of algebraic closure of $\mathbb{Q}_p$ )      72—75
Affine curve      109 145
Affine hypersurface      109 114 144
Affine space      109
Algebraic closure      53 66 73
Algebraic field extension      52
Algebraic varieties      113 114
Algebraically closed      9 72—73
Artin — Hasse exponential      93 97 143 144
Automorphism      54
Bernoulli distribution      34—35
Bernoulli numbers      22 29 36 136 137
Bernoulli numbers generalized      29—30
Bernoulli polynomials      34 41 136
Betti number      114
Binomial series      81—82
Bombieri, E.      84
Cardinality      75 140
Cardinality of Zp      19 134—135
Cauchy sequences      3 8—9 10 71—72 76
CHARACTER      29 116
Character of conductor N      29
Character, primitive      29
Characteristic of field      52
Clausen — von Staudt congruence      44 45—46 51 137
Compact-open sets      31
Compactness      31 33 57 66
Compactness, local      57—58 65—66 73
Compactness, sequential      30 139
Completeness      9 65 71—72
Completion      8 10 72 73
Conjugates      54
Conjugates, p-adic norm of      61
Continuous p-adic function      21 89
Continuous power series      78
Convergence of power series      76—77
Convergence, conditional      77
Convergence, disc of      77 83 84
Convergence, radius of      76
Cosine, p-adic      81 83 97
Deligne, P.      114
Derivative      84—85 88 138
Derivative, disc of convergence of      84
Diagonal process      134
Differentiable      85
Dirac distribution      33
Dirichlet L-functions      29—30 49—50 136
Disc, closed      77
Disc, non-Archimedean      6
Disc, open      77
Distribution, Bernoulli      34—35
Distribution, boundedly increasing      41
Distribution, Dirac      33
Distribution, Haar      32—33
Distribution, Mazur      33
Distribution, p-adic      31
Dwork      113
Dwork's lemma      93—94 97 143
Eisenstein irreducibility criterion      20 107
Eisenstein polynomial      66 69 140 143
Eisenstein series      50
ellipse      74 139
Elliptic curve      50 115 145
Entire function      107
Entire function, p-adic      122
Euler $\phi$ -function      56
Euler factor      28 43—44 50 89
Euler product      28 29
Exponential function, Artin — Hasse      93 97 143 144
Exponential function, p-adic      79 80—81 83 107
Factorial, p-adic ordinal of      7 79
Field      1
Field of p-adic numbers      10—15
Field, characteristic of      52
Field, extension      52
Field, extension, algebraic      52
Field, extension, automorphisms of      54
Field, extension, degree of      52
Field, extension, Galois      54
Field, extension, totally ramified      66
Field, extension, unramified      66—68
Field, finite      54—57
Field, finite, generator of      56 57 137—138
Field, fixed      54
Field, Galois group of      54
Field, perfect      53
Field, prime      55
Field, residue      55 65 66 69
Galois group      54
Gamma-function      22 47 88—89 91 96
Gamma-function, p-adic      89—91 96
Gauss sum      30 50 96
Gauss — Legendre multiplication formula      91
Gel'fand, I.M.      9
Generating function      110
Genus      114
Haar distribution      32—33
Hecke series      41
Hensel's lemma      16 19 67—68
Homogeneous completion      110
Homogeneous polynomial      110
Hyperbola      74 139
Hypersurface, affine      109 114 144
Hypersurface, projective      110 114 144
Ideal      63
Ideal, maximal      64
Ideal, prime      63
Index of ramification      66 74
Integral, closure      64
Integral, domain      63
Integration, p-adic      40
Interval, p-adic      30
Isosceles triangle principle      6
Katz, N.M.      50
Kazhdan, D.      61
Krasner's Lemma      69—70 74 139
Kubota, T.      28
Kummer congruences      28 44—45 51 137
L-functions      29—30 49—50 136
L-functions, p-adic      50

L-functions, value at one      50 136
Leopoldt, H.W.      28
Lifting      118
Lipschitz condition      41
Locally analytic      87 88
Locally constant      31
Logarithm, Iwasawa extension of      50 87—88 95
Logarithm, p-adic      50 77 78 79—81 100 142
Manin, Yu.I.      41
Mazur distribution      33
Mazur measure      36 44 47
Mazur — Mellin transform      47—48
Mean value theorem      85
Measure, Bernoulli      36—37
Measure, Mazur      36 44 47
Measure, p-adic      36 39
Mellin transform      47 89
Meromorphic function, p-adic      122
Metric      1
Metric, Archimedean      3
Metric, equivalent      3
Metric, non-Archimedean      3
Metric, p-adic      7 8
Metric, space      1
Modular forms      50
Modular forms, p-adic      50
Moebius function      92
Newton polygon and radius of convergence      99—100 101
Newton polygon and roots of polynomials      97—98
Newton polygon and zeros of power series      103 106
Newton polygon of logarithm      100
Newton polygon of polynomial      97—98 107 143
Newton polygon of power series      98—100 107—108 143—144
Newton's method, p-adic      17—18
Norm equivalent      3
Norm extension of      59—63
Norm non-Archimedean      3
Norm of an element      59—60
Norm on a field      1 6—7
Norm on a vector space      58—59 65—66
Norm p-adic      2 10 61 72
Norm sup-norm      58
Norm, Archimedean      3
Ostrowski's theorem      3
p-adic, continuity      21
p-adic, digits      13 14
p-adic, distribution      30
p-adic, expansion      13 68
p-adic, expansion, repeating      19 134
p-adic, expansion, terminating      19
p-adic, integer      13
p-adic, integration      40 42—44
p-adic, interpolation      21—22 26—27 46 89
p-adic, measure      36
p-adic, metric      7 8
p-adic, norm      2 10 61 72
p-adic, series      14
p-adic, unit      13
Paradoxes      82—83 84
Polynomial, homogeneous      110
Polynomial, monic irreducible      53 57
Polynomial, symmetric      64
Power series      76
Power series, derivative      84
Power series, formal      7 80 85—86 118
Primitive character      29
Primitive element      53
Projective completion      110
Projective hypersurface      110 114 144
Projective space      109
Radius of convergence      76
Ramification, index      66 74 138
Ramification, tame      67 74
Ramification, wild      67
Regularization      36
Residue field      55 65
Riemann $\zeta$ -function      21 47 89
Riemann $\zeta$ -function, functional equation      28 48
Riemann $\zeta$ -function, p-adic interpolation      21 28
Riemann $\zeta$ -function, value at 1 - 2k      28 44 48—49
Riemann $\zeta$ -function, value at 2k      24 25 136
Riemann hypothesis      114 115
Riemann sum      39
Ring      63
Ring, ideal of      63
Ring, valuation      65 68—69 72
Sequential compactness      30
Series, p-adic      14
Serre, J.-P.      50
Sine, p-adic      81 83 84 97
Space, affine      109
Space, projective      109
Square roots in $\mathbb{Q}_{p}$       15—16 19—20 83 84 135 141
Stirling's formula      29
Sup-norm      58 65 138
Symmetric polynomials      64
Teichmueller representative      14 20 67—69 72 96 116 118 124
Totally disconnected      77
Trace      116 119
Transcendence degree      75
Triangle inequality      5
Valuation ring      65 68—69 72
Vector space      57
Vector space, norm on      58—59 65—66
Weierstrass Preparation Theorem, p-adic      105 127 144
Weierstrass product      107 108
Weil Conjectures      113—114 115
Wilson's theorem      90 143
Witt vectors      69
Zeta-function of set of equations      110—111
Zeta-function of set of equations, affine line      111
Zeta-function of set of equations, affine space      114
Zeta-function of set of equations, p-adic meromorphicity      122—124
Zeta-function of set of equations, point      114
Zeta-function of set of equations, projective line      111—112
Zeta-function of set of equations, projective space      114
Zeta-function of set of equations, rationality      113—115 122—127
Zeta-function, p-adic (Kubota — Leopoldt)      44 46 47—48
Zeta-function, p-adic (Kubota — Leopoldt), branches      46
Zeta-function, p-adic (Kubota — Leopoldt), pole      46
Zeta-function, Riemann      21 47 89

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