黎曼假设的验证：李判据的应用
Toward verification of the Riemann hypothesis: Application of the Li criterion
摘要：
我们充分应用李准则的黎曼假设举行。基于序列λ k的一个级数表示，我们确定了相应的Riemann zeta函数和的新的界以及序列本身.我们发现，如果序列η_j的某些约束性质成立，则Riemann假设成立。常数η j进入zeta函数关于s=1的对数导数的Laurent展开式，并表现出显著的特征。{ \em关于我们的猜想}，不仅有Riemann假设，而且有关于zeta函数的非平凡零点的倒数幂和的不等式。
英文摘要：
We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{λ_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we determine new bounds for relevant Riemann zeta function sums and the sequence itself. We find that the Riemann hypothesis holds if certain conjectured properties of a sequence η_j are valid. The constants η_j enter the Laurent expansion of the logarithmic derivative of the zeta function about s=1 and appear to have remarkable characteristics. {\em On our conjecture}, not only does the Riemann hypothesis follow, but an inequality governing the values λ_n and inequalities for the sums of reciprocal powers of the nontrivial zeros of the zeta function.
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