多伽马理论、Li/Keiper常数和黎曼假设的有效性
Polygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis
摘要：
黎曼假设等价于控制一系列实常数的Li准则，这些实常数是黎曼xi函数在1处的某些对数导数。我们研究了一组相关的常数c_n，n = 1，2，.详细地表明λ_n/n的（1/2）ln n的主导行为在c_n中是不存在的。另外，还得到了c_n的一个新的Stieltjes常数gamma_j的显式表示，并对c_n的大n行为进行了推测。如果这个猜想成立，黎曼假设的有效性将随之而来。
英文摘要：
The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants c_n, n = 1,2,..., showing in detail that the leading behaviour (1/2) ln n of lambda_n/n is absent in c_n. Additional results are presented, including a novel explicit representation of c_n in terms of the Stieltjes constants gamma_j. We conjecture as to the large-n behaviour of c_n. Should this conjecture hold, validity of the Riemann hypothesis would follow.
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