. . . . . "En th\u00E9orie alg\u00E9brique des nombres, le th\u00E9or\u00E8me de Tchebotariov, d\u00FB \u00E0 Nikolai Tchebotariov et habituellement \u00E9crit th\u00E9or\u00E8me de Chebotarev, pr\u00E9cise le th\u00E9or\u00E8me de la progression arithm\u00E9tique de Dirichlet sur l'infinitude des nombres premiers en progression arithm\u00E9tique : il affirme que, si a, q \u2265 1 sont deux entiers premiers entre eux, la densit\u00E9 naturelle de l'ensemble des nombres premiers congrus \u00E0 a modulo q vaut 1/\u03C6(q)."@fr . . . . "Chebotarev's density theorem"@en . . "Der tschebotarjowsche Dichtigkeitssatz (je nach Transkription auch Dichtigkeitssatz von Chebotar\u00EBv oder Tschebotareff) ist eine Verallgemeinerung des Satzes von Dirichlet \u00FCber Primzahlen in arithmetischen Progressionen auf Galoiserweiterungen von Zahlk\u00F6rpern. Im Falle einer abelschen Erweiterung von erh\u00E4lt man daraus den Satz zur\u00FCck, dass die Menge der Primzahlen der Form , hat, wobei f\u00FCr die Eulersche Phi-Funktion steht. In seiner allgemeinen Form folgt daraus insbesondere der 1880 von Kronecker bewiesene Satz, dass genau der Primzahlen in einer gegebenen Galoiserweiterung von vom Grad sind. Der Satz wurde von Nikolai Grigorjewitsch Tschebotarjow im Jahr 1922 gefunden und 1923 erstmals auf russisch, 1925 auf deutsch ver\u00F6ffentlicht."@de . . . "Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K. There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime p in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes p less than a large integer N, tends to a certain limit as N goes to infinity. It was proved by Nikolai Chebotaryov in his thesis in 1922, published in."@en . . . "Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K. There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime p in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes p less than a large integer N, tends to a certain limit as N goes to infinity. It was proved by Nikolai Chebotaryov in his thesis in 1922, published in. A special case that is easier to state says that if K is an algebraic number field which is a Galois extension of of degree n, then the prime numbers that completely split in K have density 1/n among all primes. More generally, splitting behavior can be specified by assigning to (almost) every prime number an invariant, its Frobenius element, which is a representative of a well-defined conjugacy class in the Galois group Gal(K/Q). Then the theorem says that the asymptotic distribution of these invariants is uniform over the group, so that a conjugacy class with k elements occurs with frequency asymptotic to k/n."@en . . "\u4EE3\u6570\u7684\u6574\u6570\u8AD6\u306E\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306E\u5BC6\u5EA6\u5B9A\u7406\uFF08\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306E\u307F\u3064\u3069\u3066\u3044\u308A\u3001\u82F1: Chebotarev's density theorem\uFF09\u3068\u306F\u3001\u6709\u7406\u6570\u4F53 \u306E\u30AC\u30ED\u30A2\u62E1\u5927 K \u306B\u304A\u3051\u308B\u7D20\u6570\u306E\u5206\u89E3\u306E\u4ED5\u65B9\u306B\u3064\u3044\u3066\u6210\u308A\u7ACB\u3064\u7D71\u8A08\u7684\u306A\u6CD5\u5247\u3092\u660E\u3089\u304B\u306B\u3057\u305F\u5B9A\u7406\u3067\u3042\u308B\u3002\u4E00\u822C\u306B\u3001\u7D20\u6570\u306FK\u306E\u4EE3\u6570\u7684\u6574\u6570\u306E\u74B0\u3067\u3044\u304F\u3064\u304B\u306E\u7406\u60F3\u56E0\u5B50\u306B\u5206\u89E3\u3057\u3001\u8D77\u3053\u308A\u3046\u308B\u5206\u89E3\u306E\u30D1\u30BF\u30FC\u30F3\u306F\u6709\u9650\u3067\u3042\u308B\u3002\u4E00\u822C\u306E\u30AC\u30ED\u30A2\u62E1\u5927\u306B\u304A\u3044\u3066\u7D20\u6570p \u304C\u3069\u3046\u5206\u89E3\u3059\u308B\u304B\u5B8C\u5168\u306B\u8A18\u8FF0\u3059\u308B\u3053\u3068\u306F\u5927\u304D\u306A\u672A\u89E3\u6C7A\u554F\u984C\u3067\u3042\u308B\u304C\u3001\u6574\u6570N\u672A\u6E80\u306E\u7D20\u6570 p \u3067\u4E0E\u3048\u3089\u308C\u305F\u30D1\u30BF\u30FC\u30F3\u3067\u5206\u89E3\u3059\u308B\u3082\u306E\u306E\u5272\u5408\u306F\u3001N\u3092\u9650\u308A\u306A\u304F\u5927\u304D\u304F\u3057\u3066\u3044\u3063\u305F\u3068\u304D\u3042\u308B\u6975\u9650\u306B\u53CE\u675F\u3059\u308B\u3053\u3068\u304C\u8A3C\u660E\u3055\u308C\u305F\u3002\u3053\u308C\u3092\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306E\u5BC6\u5EA6\u5B9A\u7406\u3068\u3044\u3046\u3002\u3053\u306E\u3053\u3068\u306F\u30CB\u30B3\u30E9\u30A4\u30FB\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306B\u3088\u3063\u30661922\u5E74\u306B\u5F7C\u306E\u5B66\u4F4D\u8AD6\u6587\u306B\u3066\u8A3C\u660E\u3055\u308C\u3001 \u3067\u516C\u8868\u3055\u308C\u305F\u3002 \u7C21\u5358\u306A\u5834\u5408\u306B\u3064\u3044\u3066\u3053\u306E\u5B9A\u7406\u306E\u5185\u5BB9\u3092\u8FF0\u3079\u308B\u3068\u3001\u6709\u7406\u6570\u4F53\u306En \u6B21\u30AC\u30ED\u30A2\u62E1\u5927\u3067\u3042\u308B\u4EE3\u6570\u4F53K\u306B\u304A\u3044\u3066\u5B8C\u5168\u5206\u89E3\u3059\u308B\u7D20\u6570\u306E\u7D20\u6570\u5168\u4F53\u306E\u4E2D\u3067\u306E\u5BC6\u5EA6\u306F 1/n \u3067\u3042\u308B\u3001\u3068\u306A\u308B\u3002\u4E00\u822C\u306B\u306F\u3001\u30D5\u30ED\u30D9\u30CB\u30A6\u30B9\u5143\u3068\u547C\u3070\u308C\u308B\u30AC\u30ED\u30A2\u7FA4 Gal(K/Q) \u306E\u5143\u304C\uFF08\u307B\u3068\u3093\u3069\uFF09\u5168\u3066\u306E\u7D20\u6570\u306B\u5BFE\u3057\u3066\u5171\u5F79\u3092\u9664\u3044\u3066\u5B9A\u307E\u308A\u3001\u3053\u306E\u4E0D\u5909\u91CF\u304C\u7D20\u6570\u306E\u5206\u89E3\u306E\u4ED5\u65B9\u3092\u6C7A\u5B9A\u3057\u3066\u3044\u308B\u3002\u3053\u306E\u3068\u304D\u3001\u5BC6\u5EA6\u5B9A\u7406\u306E\u4E3B\u5F35\u306F\u3001\u3053\u306E\u4E0D\u5909\u91CF\u304C\u30AC\u30ED\u30A2\u7FA4\u306E\u4E2D\u3067\u4E00\u69D8\u306B\u6F38\u8FD1\u5206\u5E03\u3057\u3001\u3057\u305F\u304C\u3063\u3066 k \u500B\u306E\u5143\u304B\u3089\u306A\u308B\u5171\u5F79\u985E\u306B\u5165\u308B\u983B\u5EA6\u306F\u6F38\u8FD1\u7684\u306B\u306F k/n \u3067\u3042\u308B\u3001\u3068\u3044\u3046\u3082\u306E\u3067\u3042\u308B\u3002"@ja . . . . . . . . . . . . . . . . . . . . . . . . "Th\u00E9or\u00E8me de densit\u00E9 de Tchebotariov"@fr . "1093210136"^^ . . "Tschebotarjowscher Dichtigkeitssatz"@de . . . . "\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306E\u5BC6\u5EA6\u5B9A\u7406"@ja . . "535349"^^ . . . . . "\u4EE3\u6570\u7684\u6574\u6570\u8AD6\u306E\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306E\u5BC6\u5EA6\u5B9A\u7406\uFF08\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306E\u307F\u3064\u3069\u3066\u3044\u308A\u3001\u82F1: Chebotarev's density theorem\uFF09\u3068\u306F\u3001\u6709\u7406\u6570\u4F53 \u306E\u30AC\u30ED\u30A2\u62E1\u5927 K \u306B\u304A\u3051\u308B\u7D20\u6570\u306E\u5206\u89E3\u306E\u4ED5\u65B9\u306B\u3064\u3044\u3066\u6210\u308A\u7ACB\u3064\u7D71\u8A08\u7684\u306A\u6CD5\u5247\u3092\u660E\u3089\u304B\u306B\u3057\u305F\u5B9A\u7406\u3067\u3042\u308B\u3002\u4E00\u822C\u306B\u3001\u7D20\u6570\u306FK\u306E\u4EE3\u6570\u7684\u6574\u6570\u306E\u74B0\u3067\u3044\u304F\u3064\u304B\u306E\u7406\u60F3\u56E0\u5B50\u306B\u5206\u89E3\u3057\u3001\u8D77\u3053\u308A\u3046\u308B\u5206\u89E3\u306E\u30D1\u30BF\u30FC\u30F3\u306F\u6709\u9650\u3067\u3042\u308B\u3002\u4E00\u822C\u306E\u30AC\u30ED\u30A2\u62E1\u5927\u306B\u304A\u3044\u3066\u7D20\u6570p \u304C\u3069\u3046\u5206\u89E3\u3059\u308B\u304B\u5B8C\u5168\u306B\u8A18\u8FF0\u3059\u308B\u3053\u3068\u306F\u5927\u304D\u306A\u672A\u89E3\u6C7A\u554F\u984C\u3067\u3042\u308B\u304C\u3001\u6574\u6570N\u672A\u6E80\u306E\u7D20\u6570 p \u3067\u4E0E\u3048\u3089\u308C\u305F\u30D1\u30BF\u30FC\u30F3\u3067\u5206\u89E3\u3059\u308B\u3082\u306E\u306E\u5272\u5408\u306F\u3001N\u3092\u9650\u308A\u306A\u304F\u5927\u304D\u304F\u3057\u3066\u3044\u3063\u305F\u3068\u304D\u3042\u308B\u6975\u9650\u306B\u53CE\u675F\u3059\u308B\u3053\u3068\u304C\u8A3C\u660E\u3055\u308C\u305F\u3002\u3053\u308C\u3092\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306E\u5BC6\u5EA6\u5B9A\u7406\u3068\u3044\u3046\u3002\u3053\u306E\u3053\u3068\u306F\u30CB\u30B3\u30E9\u30A4\u30FB\u30C1\u30A7\u30DC\u30BF\u30EC\u30D5\u306B\u3088\u3063\u30661922\u5E74\u306B\u5F7C\u306E\u5B66\u4F4D\u8AD6\u6587\u306B\u3066\u8A3C\u660E\u3055\u308C\u3001 \u3067\u516C\u8868\u3055\u308C\u305F\u3002 \u7C21\u5358\u306A\u5834\u5408\u306B\u3064\u3044\u3066\u3053\u306E\u5B9A\u7406\u306E\u5185\u5BB9\u3092\u8FF0\u3079\u308B\u3068\u3001\u6709\u7406\u6570\u4F53\u306En \u6B21\u30AC\u30ED\u30A2\u62E1\u5927\u3067\u3042\u308B\u4EE3\u6570\u4F53K\u306B\u304A\u3044\u3066\u5B8C\u5168\u5206\u89E3\u3059\u308B\u7D20\u6570\u306E\u7D20\u6570\u5168\u4F53\u306E\u4E2D\u3067\u306E\u5BC6\u5EA6\u306F 1/n \u3067\u3042\u308B\u3001\u3068\u306A\u308B\u3002\u4E00\u822C\u306B\u306F\u3001\u30D5\u30ED\u30D9\u30CB\u30A6\u30B9\u5143\u3068\u547C\u3070\u308C\u308B\u30AC\u30ED\u30A2\u7FA4 Gal(K/Q) \u306E\u5143\u304C\uFF08\u307B\u3068\u3093\u3069\uFF09\u5168\u3066\u306E\u7D20\u6570\u306B\u5BFE\u3057\u3066\u5171\u5F79\u3092\u9664\u3044\u3066\u5B9A\u307E\u308A\u3001\u3053\u306E\u4E0D\u5909\u91CF\u304C\u7D20\u6570\u306E\u5206\u89E3\u306E\u4ED5\u65B9\u3092\u6C7A\u5B9A\u3057\u3066\u3044\u308B\u3002\u3053\u306E\u3068\u304D\u3001\u5BC6\u5EA6\u5B9A\u7406\u306E\u4E3B\u5F35\u306F\u3001\u3053\u306E\u4E0D\u5909\u91CF\u304C\u30AC\u30ED\u30A2\u7FA4\u306E\u4E2D\u3067\u4E00\u69D8\u306B\u6F38\u8FD1\u5206\u5E03\u3057\u3001\u3057\u305F\u304C\u3063\u3066 k \u500B\u306E\u5143\u304B\u3089\u306A\u308B\u5171\u5F79\u985E\u306B\u5165\u308B\u983B\u5EA6\u306F\u6F38\u8FD1\u7684\u306B\u306F k/n \u3067\u3042\u308B\u3001\u3068\u3044\u3046\u3082\u306E\u3067\u3042\u308B\u3002"@ja . "13067"^^ . . "En th\u00E9orie alg\u00E9brique des nombres, le th\u00E9or\u00E8me de Tchebotariov, d\u00FB \u00E0 Nikolai Tchebotariov et habituellement \u00E9crit th\u00E9or\u00E8me de Chebotarev, pr\u00E9cise le th\u00E9or\u00E8me de la progression arithm\u00E9tique de Dirichlet sur l'infinitude des nombres premiers en progression arithm\u00E9tique : il affirme que, si a, q \u2265 1 sont deux entiers premiers entre eux, la densit\u00E9 naturelle de l'ensemble des nombres premiers congrus \u00E0 a modulo q vaut 1/\u03C6(q)."@fr . "Der tschebotarjowsche Dichtigkeitssatz (je nach Transkription auch Dichtigkeitssatz von Chebotar\u00EBv oder Tschebotareff) ist eine Verallgemeinerung des Satzes von Dirichlet \u00FCber Primzahlen in arithmetischen Progressionen auf Galoiserweiterungen von Zahlk\u00F6rpern. Im Falle einer abelschen Erweiterung von erh\u00E4lt man daraus den Satz zur\u00FCck, dass die Menge der Primzahlen der Form , hat, wobei f\u00FCr die Eulersche Phi-Funktion steht. In seiner allgemeinen Form folgt daraus insbesondere der 1880 von Kronecker bewiesene Satz, dass genau der Primzahlen in einer gegebenen Galoiserweiterung von vom Grad sind."@de . . . . . . . . . . . . . . .