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問題 · 2026-05-17
黎曼猜想的零點是黎曼ζ函數的複數解，分為平凡零點和非平凡零點，猜想主張所有非平凡零點的實部都等於1/2。
黎曼猜想涉及黎曼ζ函數ζ(s)=0的複數解，稱為零點[1][2]。這些零點分為兩類：平凡零點位於負偶數s=-2,-4,-6,…上[1][2]；非平凡零點則落在複平面的臨界帶0<Re(s)<1內[1][2]。黎曼猜想的核心主張是所有非平凡零點的實部都等於1/2，即都在直線Re(s)=1/2上，這條線被稱為臨界線[1][2]。這些零點與質數分布有深刻的數學聯繫[2]。儘管電腦已驗證了數萬億個非平凡零點都落在臨界線上，但至今仍缺乏嚴謹的普遍性證明[2]。
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