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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Barban–Davenport–Halberstam theorem ： ウィキペディア英語版 Barban–Davenport–Halberstam theorem In mathematics, the Barban–Davenport–Halberstam theorem is a statement about the distribution of prime numbers in an arithmetic progression. It is known that in the long run primes are distributed equally across possible progressions with the same difference. Theorems of the Barban–Davenport–Halberstam type give estimates for the error term, determining how close to uniform the distributions are. ==Statement== Let ''a'' be coprime to ''q'' and :$\backslash vartheta(x;q,a)\; =\; \backslash sum\_\; \backslash log\; p\; \backslash$ be a weighted count of primes in the arithmetic progression ''a'' mod ''q''. We have :$\backslash vartheta(x;q,a)\; =\; \backslash frac\; +\; E(x;q,a)\; \backslash$ where ''φ'' is Euler's totient function and the error term ''E'' is small compared to ''x''. We take a sum of squares of error terms :$V(x,Q)\; =\; \backslash sum\_\; \backslash sum\_)\; \backslash$ for $1\; \backslash leq\; Q\; \backslash leq\; x$ and every positive ''A'', where ''O'' is Landau's Big O notation. This form of the theorem is due to Gallagher. The result of Barban is valid only for $Q\; \backslash leq\; x\; (\backslash log\; x)^$ for some ''B'' depending on ''A'', and the result of Davenport–Halberstam has ''B'' = ''A'' + 5. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Barban–Davenport–Halberstam theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.