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Tanigawa Y. — Number Theory: Tradition and Modernization
Tanigawa Y. — Number Theory: Tradition and Modernization

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Название: Number Theory: Tradition and Modernization

Автор: Tanigawa Y.

Аннотация:

"Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. The chapters presented are quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects." This book is intended for researchers and graduate students in analytic number theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 260

Добавлена в каталог: 12.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\bar{\gamma},\varepsilon)$-cone      30
$\gamma$-function, automorphic      120
$\gamma$-function, Dirichlet      229
$\gamma$-function, factorization of      121
$\gamma$-function, Hecke      156
$\gamma$-function, nontrivial zeros of      125 128
$\gamma$-function, primitive      120
$\gamma$-function, Rankin — Selberg      121 129.181
$\gamma$-function, trivial zeros of      133
Adele ring      122
Admissible n-tuple, $(N_1, ..., N_n)$      32
Analytic continuation      154
Apery, R,      100
Apostol — Vu multiple series      157
Artin hypotheses      30
Artin’s conjecture for primitive roots      13
Base change      120 121
Basis      27
Bernoulli, number      210
Bernoulli, polynomial      154 210
Beta-expansion      1
Bombieri — Vinogradov typo mean-value theorem      41
Canonical number system      1
Characteristic of vectors      29
Class field theory      120
Class number      102
Cochrane sum      234
Cochrane sum, k-dimensional      235
Combinatorial sieving      125
Completely split primes      122
Congruences for Euler polynomials      206
Cubic field      175 176
Cubic field,cyclic      176 177 180
Cusp form      23
D.H.Lehmer’s problem      229
Decimal expansion      68 73
Dedekind, eta-function      108
Dedekind- sum      232
Deligne’s theorem      25
density      65
Density-function      70 73
Dirac mass      124
Dirichlet character      155 l59
Distribution density      75
Elliptic curve      175
Elliptic curve, supersingular      98
Elliptic transformation      188
Equi-distribution property      12
Essouabri’s theorem      163
Estimate of the trigonometric integral      34
Euler product      122
Euler — Maclaurin summation formula      154
Euler — Zagier r-fold sum      153
Euler, L.      153 205
Euler, number      206
Euler-polynomial      206
Explicit formula      128 129
Exponential sum      44 187
Exponential sum in arithmetic progression      44
Fermat curve      176
Finite theta series      187
Functional equation      88 104 12?
Functional relation      161
Gauss circle problem      219
Gaussian sum, classical      48
Gaussian sum, generalization of      48
Generalized Riemann Hypothesis (GRH)      12
GENERIC      177 180
Goldbach — Vinogradov Theorem      39
GUE model      120
Haase invariant      102
Handelman, D.      5
Hasse, H.      13
Hauptmodul      99
Hecke algebra      81
Heeke, congruence subgroup      23
Heeke, eigen form      25
Heeke, operator      21
Hilbert — Kamke problem      28
Honley, C.      13
Hua’s problem      34
Hypothesis II      120 121 123 149
Klein, F.      98
Kloosterman sum      236
Kratzel, E.      219
Lagarias, J.C. and Odlyzko, A.M.      16
Langlands correspondence      122
Langlands’ funetoriality conjecture      120
Local density      84
Local L-factor      122
Mean value of the Cochrane sums      235
Mean value of the Dedekind sums      232
Mean value theorem      32
Mellin — Barnes integral formula      154
Meromorphic continuation      154
method of Mordell      183
Modular degree      122
Modular relation      104
Mordell curve      176 182
Mordell — Tornheim multiple series      157
Mordell — Weil rank      180 181
Mortens’ theorem      121
Multiple, character sum      155
Multiple, Dirichlet series      156
Multiple, L-series      156
Multiple, polylogarithms      1157
Multiple, strip      162
Multiplicative order      11
Multivariate, Tarry problem      35
Multivariate, Vinogradov problem      35
n-level correlation      120
Natural density      11
New form      23
Noncyclic extension field      121
Normal distribution      70 74
Odoni, R.W.      13
Old form      23
Order condition      28
Order of ramification      122
p-solvability condition      31
Parabolic transformation      188
Perron — Frabenius theorem      5
Pisot number      2
Point at infinity      177
Prehomogeneous vector space      93
primitive      103
q-adic integer      206
q-series identities of Ramanujan      104
Quasi modular      97
Rademacher, H.      40
Ramanujan conjecture      123
Ramanujan, S.      98
Ramanujan’s formula      111
Real quadratic field      15G
Real solvability condition      31
Recursive structure      159 163
Relative invariant      82
Representation, contragradient      127
Representation, cuspidal      120
Representation, self-contragredient      131 134
Residual index      12
Riemann hypothesis      125
Rogers — Ramanujan function      98
Selberg orthogonality      120 131 126 131
Set partition      126
Short form      179—181
Short interval      220
Siegel C.L.      5
Singular series      42 63
Singularities      154
Spherical function      82
Square-free integer      220
Super singular      101
Superposition distribution      120
The partial fraction expansion for the coth      113
Theory of multiple trigonometric sum with primes      36
Theta reciprocation      187
Theta-Weyl sum      188
Theta-Weyl sum, cubic      191
Theta-Weyl sum, quadratic      188
Three Primes Theorem      39
Torsion part      1S2
Trigonometrical sum      187
Truncated Chebyshev function      57
Type (F)      83
Uniform distribution      74
Universality of the n-level correlation      12
van der Corput method      187 201
van der Corput, J.G.      187
van der Corput, reciprocal function      186
Vinogradov, I.M.      39 187
Vinogradov, method      201
Vinogradov, problem      30
Vinogradov, system of equations      30
Waring problem      28
Weyl sum      187
Weyl — Hardy — Littlewood method      201
Weyl, H.      187
Zagier, D.      153
Zero-free region      131
Zero-free region, Barnes multiple      156
Zero-free region, double Hurwitz — Lerch      161
Zero-free region, Hecke      156
Zero-free region, Hurwitz — Lerch      104 161
Zero-free region, Lerch      161
Zero-free region, Shintani      157
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