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Neukrich J. — Algebraic number theory
Neukrich J. — Algebraic number theory



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Название: Algebraic number theory

Автор: Neukrich J.

Аннотация:

From the review: "The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner... The author discusses the classical concepts from the viewpoint of Arakelov theory.... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples.... The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook.... The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available."
W. Kleinert in: Zentralblatt für Mathematik, 1992


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 588

Добавлена в каталог: 14.09.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Topology, Zariski      85
Totally disconnected      264
Totally ramified      49 158 286
Totally split      49
Trace      8 444
Trace form      194
Trace-zero hyperplane      39
Trace-zero space      460
TRANSFER      296 410
Transfer on Witt vectors      134
Transformation formula for theta series      425 437 438 439 452 490
Trivial character      434
Trivial metric      227 229
Trivial zeroes of the Riemann's zeta function      432
Type of a Grobencharacter      478
Unique prime decomposition      18
UNITS      39
Units, cyclotomic      44
Units, Dirichlet's unit theorem      42 81 358
Units, fundamental      42
Units, Gaussian      3
Units, p-adic      112
Units, principal      122
Units, S-units      71 358
Units, Shintani's unit theorem      507
Units, unit lattice      40
Units, unit rank, p-adic      394
Universal covering      93
Universal norms      304 308
Unramified      49 184 202 286 309
Unramified, $\mathbb{C}|\mathbb{R}$ is unramified      184 220 224
Unramified, extension of algebraic number fields      202
Unramified, extension of henselian fields      153
Unramified, maximal extension      154 285
Upper half-plane      425
Upper half-space      445
Upper numbering of ramification groups      180
Valuation      67 116
Valuation ring      121
Valuation ring, henselian      143
Valuation theory      99
Valuation theory, abstract      284 309
Valuation, abstract henselian      288 309 389
Valuation, archimedean      118
Valuation, degree valuation      95
Valuation, discrete      67 95 121
Valuation, discrete valuation ring      67
Valuation, equivalent valuations      116
Valuation, exponential      69 107 120 184
Valuation, extension of      131 144
Valuation, henselian      143 288 309 389
Valuation, henselian P-valuation      298
Valuation, Krull valuation      123
Valuation, nonarchimedean      118
Valuation, normalized      121 184
Valuation, p-adic      69
Values (special) of Dirichlet L-series      442 443 515
Values (special) of Riemann's zeta function      427 431 432
Vandermonde matrix      11
Vector bundle      193 255
ver      296 410
Weber function      403
Weber, H.      366 405
Weierstrass $\wp$-function      401
Weierstrass preparation theorem      116
Wildly ramified      158
Wiles, A.      38
Wilson's theorem      2
Witt vectors      134 283 340
Witt, E.      410
Zagier, D.      433
Zahlbericht, Hasse's      363
Zariski topology      85
Zeroes of Artin L-series      541
Zeroes of Dirichlet L-series      442
Zeroes of Riemann's zeta function      432
Zeta function      419
Zeta function, completed      422 466
Zeta function, Dedekind      457
Zeta function, p-adic      516
Zeta function, partial      458
Zeta function, Riemann      419
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