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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Koblitz N. - p-adic numbers, p-adic analysis, and zeta-functions |
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| Предметный указатель |
 (p-adic ordinal) 2 66 72
 (completion of algebraic closure of  ) 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  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 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, conditional 77
Convergence, disc of 77 83 84
Convergence, of power series 76-77
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
Differentiate 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,  -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, 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, of p-adic numbers 10-15
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
Krasnefs 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, p-adic 50 77 78 79-81 100 142
Logarithm, p-adic, Iwasawa extension of 50 87-88 95
Manin, Yu.I. 41
Mazur - Mellin transform 47-48
Mazur, distribution 33
Mazur, measure 36 44 47
Mean value theorem 85
Measure, p-adic 36 39
Measure, p-adic, Bernoulli 36-37
Measure, p-adic, Mazur 36 44 47
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
Mobius function 92
Modular forms 50
Modular forms, p-adic 50
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, Archimedean 3
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
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,  -function 21 47 89
Riemann, -function, functional equation 28 48
Riemann, -function, p-adic interpolation 21 28
Riemann, -function, value at 1 - 2k 28 44 48-49
Riemann, -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 15-16 19-20 83 84 135 141
Stirling's formula 29
Sup-norm 58 65 138
Symmetric polynomials 64
Teichmuller 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 113-115 122-127 150
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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