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arXiv 2307.020272023-07-05math.NTmath.PR

Selberg 类中 $L$-函数中心零点的一种概率解释

A probabilistic interpretation for central zeros of $L$-functions in the Selberg class

Takashi Nakamura, Masatoshi Suzuki

备注：: 6 pages

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AI总结：

本文通过无穷可分分布给出 Selberg 类 $L$-函数黎曼假设的等价条件，从而为中心零点建立概率解释。

摘要：

我们通过用无穷可分分布表述 Selberg 类中 $L$-函数的黎曼假设的一个等价条件，证明了这些 $L$-函数的中心零点具有一种概率解释。

英文摘要：

We show that central zeros of $L$-functions in the Selberg class have a probabilistic interpretation by stating an equivalence condition of the Riemann hypothesis for the $L$-functions in terms of infinitely divisible distributions.

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