黎曼假设的Beurling实变量变换的算术性质
Arithmetical Aspects of Beurling's Real Variable Reformulation of the Riemann Hypothesis
摘要：
基于Moebius数的经典组合恒等式的综合形式，给出了Nyman-Beurling等价与黎曼假设的两个算术形式，并通过经典的准初等数论方法得到了证明.这些证明还揭示了许多自然Beurling函数序列在逐点和L1范数下都趋向于（0，1）的指示函数，但在L2范数下不收敛的现象。
英文摘要：
The paper presents two arithmetical versions of the Nyman-Beurling equivalence with the Riemann hypothesis, proved by classical, quasi elementary, number-theoretic methods, based on an integrated version of the classical combinatorial identity for Moebius numbers. These proofs also give insight into the troublesome phenomenon that many natural sequences of Beurling functions tending to the indicator function of (0,1) both pointwise and in L1 norm do not converge in L2 norm.
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