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The Wiener–Ikehara theorem is a Tauberian theorem introduced by . It follows from Wiener's Tauberian theorem, and can be used to prove the prime number theorem (PNT) (Chandrasekharan, 1969). == Statement == Let ''A''(''x'') be a non-negative, monotonic nondecreasing function of ''x'', defined for 0 ≤ ''x'' < ∞. Suppose that : converges for ℜ(''s'') > 1 to the function ''ƒ''(''s'') and that ''ƒ''(''s'') is analytic for ℜ(''s'') ≥ 1, except for a simple pole at ''s'' = 1 with residue 1: that is, : is analytic in ℜ(''s'') ≥ 1. Then the limit as ''x'' goes to infinity of ''e''−''x'' ''A''(''x'') is equal to 1. 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「Wiener–Ikehara theorem」の詳細全文を読む スポンサード リンク
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