送交者: Yush 于 2005-11-08, 03:59:06:
回答: 一点补充 由 eng 于 2005-11-08, 03:09:51:
蒋的结论是，zeta函数根本没有零点：
ζ(1/2+ti)～0但≠0
ζ(δ+ti)≠0，其中δ≥0
从蒋的一篇英文论文上看，黎曼假设好象分两步：
1. zeta函数有无限多非平凡零点
2. 所有非平凡零点的实部为1/2
蒋的结论把1否定了，自然也把2也否定了。
1914年已经证明Re(s)=1/2上有无限多个零点，蒋的英文论文上也提到了其它最新的证明，但蒋认为与黎曼假设有关的计算、定理、猜想都是错的。
蒋的英文论文：
Riemann conjectured that ζ(s) has infinitely many zeros in 0 ≤σ≤1, called the critical strip. Riemann further made the remarkable conjecture that the zeros of ζ(s) in the critical strip all lie on the central line σ=1/2, a conjecture called the famous Riemann hypothesis (RH).
It was stated by Hardy in 1914 that infinitely many zeros lie on the line; A. Selberg stated in 1942 that a positive proportion at least of all the zeros lie on the line; Levinson stated in 1974 that more than one
third of the zeros lie on the line; Conrey stated in 1989 that at least two fifths of the zeros lie on the line.
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