Panchishkin A.A. — Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms :: Электронная библиотека попечительского совета мехмата МГУ

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Panchishkin A.A. — Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms

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Название: Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms

Автор: Panchishkin A.A.

Аннотация:

The main subject of the book is the arithmetic of zeta functions of automorphic forms. More precisely, it looks at p-adic properties of the special values of these functions. For the Riemann-zeta function this goes back to the classical Kummer congruences for Bernoulli numbers and their p-adic analytic continuation of the standard zeta functions of Siegel and modular forms and of the convolutions of Hilbert modular forms. The book is addressed to specialists in representation theory, functional analysis and algebraic geometry. Together with new results, it provides considerable background information on p-adic measures, their Mellin transforms, Siegel and Hilbert modular forms, Hecke operators acting on them, and Euler products.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1991

Количество страниц: 160

Добавлена в каталог: 09.10.2010

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Предметный указатель

${C}^{\infty}$ -modular form      70 77 90 100
Analytic function, bounded Cp-analytic function      24 26 82 85
Analytic function, p-adic analytic function      13
Bernoulli distribution      17
Bernoulli number, generalized Bernoulli number      18 20
Bounded Cp-analytic function      24 26 82 85
Bounded Cp-valued measure      82 86 109 125
Bounded growth, function of bounded growth      71
Compatibility criterion for distributions      17
Complex valued distribution      9 29 86 87 88
Confluent hypergeometric function      60 64
Congruence subgroup      82 91
Convolution of distributions      25
Diricblet L-function, normalized Dirichlet L-function      65 67 69 107 112
Dirichlet character      2 3 24 51 53 82 83 86 88 112
Dirichlet L-series      2 112
Distribution on a profinite set      16
Distribution, distribution on Galois group      126
Distribution, normalized distributions      92 94 115
Distribution, regularized distributions      109 117
Domain of definition of p-adic zeta-functions      2 23 81 117 125
Eisenstein series, Eisenstein series in the Hilbert modular case      131
Eisenstein series, Fourier expansion of the Siegel — Eisenstein series      60 64 67
Eisenstein series, Klingen — Eisenstein series      58 72
Eisenstein series, Normalized Eisenstein series in the Hilbert modular case      135 140
Eisenstein series, Normalized Siegel — Eisenstein series      66 67 94 100
Eisenstein series, Siegel — Eisenstein series      50 53 54 72 81 83 90
Factorization of Hecke polynomials      49
Fourier expansion of Eisenstein series in the Hilbert modular case      131
Fourier expansion of the Siegel — Eisenstein series      60 64 67
Fourier expansion, positivity property of Fourier expansion      98
Frobenius operator      35 47 91
Function of bounded growth      71
Function of moderate growth      71
Gauss sum      84 86 109 112
Gauss sum of degree m      86
Gauss sum over a totally real field      123
Generalized Bernoulli number      18 20
Heche operator      46 85 121
Hecke algebra, eigenfunction of global Hecke algebra      3 82 85
Hecke algebra, global Hecke algebra      40 82 85 122
Hecke algebra, local Hecke algebras      87
Hecke character of Unite order      6 116
Hecke couple      45
Hecke L-function      116
Hecke polynomial      41
Hecke polynomial, factorization of Hecke polynomials      49
Hilbert automorphic forms, Former expansion of Hilbert automorphic form      121
Hilbert automorphic forms, Hilbert automorphic forms of holomorphic type      6 117 121 j
Hilbert cusp form, primitive Hilbert cusp form      6 116 123
Hilbert modular forms      6 117 120
Hilbert modular forms, Non-Archimedean convolution of Hilbert modular forms      6 117 124
Hilbert modular forms, root number for Hilbert modular forms      123 128
Hilbert modular forms, twist operator for Hilbert modular forms      123
Holomorphic projection operator (Hol)      70 77 99 136
Inertial degree      10
Integral representation for the Rankin zeta function      56
Integral representation of Rankin — Shimura      131 134
Interpolation series, Mahler's interpolation theorem (Mahler's criterion)      13
Interpolation series, theorem on analyticity of interpolation series      14
Iwasawa algebra      9 22
Klingen — Eisenstein series      58 72

Kubota — Leopoldt zeta function      27 112
Kummer congruences, abstract (generalized) Kummer congruences      9 19 113 116
Maass differentioal operator      63 77
Mahler's interpolation theorem (Mahler's criterion)      13
Measure on aproSnite set      18
Measure, Mazur measure      20 27 112 113
Mellin transform, non-Archimedean S-adic Mellin transform      9 22 24 81 82 125
Modular form, $({C}^{\infty})$ modular form      70 77 90 100
Modular form, Hilbert modular form      6 117 120
Modular form, Siegel modular form      37 82 87
Newton polygon      15 16 24
Non-Archimedean analytic functions      25
Non-Archimedean convolutions of Hilbert modular forms      6 117 124
Non-Archimedean S-adic Mellin transform      9 22 24 81 82 125
Non-Archimedean standard zeta functions $({\mathcal D}^{c+}(x, f), {\mathcal D}^{c-}(x, f))$       81 85
Normalized Dirichlet L-function      65 67 69 107 112
Normalized distributions      92 94 115
Normalized Eisenstein series (in the Hilbert modular case)      135 140
Normalized Siegel — Eisenstein series G*(z, s)      66 67 94 100
Normalizing factors      67 70 93 115
p-adic analytic function      13
p-adic function, continuous modular form      12
p-adic power series      13
p-adic zeta function, domain of definition of ${C}^{\infty}$ -modular form      2 23 81 117 125
p-ordinary cusp form      4 7 84 117
Petersson scalar product (inner product)      38 70 81 91 116 122
Poincare series      72 137
Positivity property of the Fourier expansion      98
Primitive Hilbert cusp form      6 116 123
Ramification index      9
Rankin zeta function (Rankin type convolution ofSiegel modular forms)      50 87
Rankin — Shimura, integral representation of Rankin — Shimura      131 134
Regularized distributions      109 117
Regularizing factors      109 110
Root numbers (for Hilbert modular forms)      123 128
S-adic Mellin transform      9 22 24 81 125
S-adic numbers      11
Satake q-parameters      5 40 42 49 82
Siegel cusp form      38 81 83 86
Siegel modular form      37 82 87
Siegel modular form, Fourier expansion of Siegel modular form      3 46 82
Siegel upper half plane      4 34
Siegel — Eisenstein series      54 81 83 90
Siegel — Eisenstein series, normalized Siegel — Eisenstein series (G*(z, s))      94 100
Spinor zeta function      6 42 50 85
Standard zeta function $({\mathcal D}(s, f, \chi ))$       3 4 42 43 81 82
Standard zeta function $({\mathcal D}(s, f, \chi ))$ , analytic properties of the standard zeta function      83 100
Standard zeta function $({\mathcal D}(s, f, \chi ))$ , non-Archimedean standard zeta functions $({\mathcal D}^{c+}(x, f), {\mathcal D}^{c-}(x, f))$       81 85
Standard zeta function $({\mathcal D}(s, f, \chi ))$ , normalized standard zeta functions $({\mathcal D}^{*}(s, f, \chi), {\mathcal D}^{+}(s, f, \chi), {\mathcal D}^{-}(s, f, \chi))$       3 81 83 86 92 100
Standard zeta function $({\mathcal D}(s, f, \chi ))$ , special values of the standard zeta functions      83 85 92
Symplectic group      35
Tate field      2 9 12 23 81 125
TeichmiiUer representative      10
Theorem on analyticity of interpolation series      14
Theorem, Weierstrass preparation theorem      15 24
Theta series      50 88
Totally ramified extension      10
Trace operator      90 134
Twist operator (for Hilbert modular forms)      123
Unramified extension      10
Weierstrass preparation theorem      15 24
Weyl group      40 49
Whittaker function      131

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