概率重整化与解析延拓
Probabilistic renormalization and analytic continuation
摘要：
我们介绍了一个理论的概率重整化系列，重整化的值被编码在一个特定的随机变量的期望的集合上的自然数。我们确定了一个大类的弱重正化Dirichlet型级数，其分析取决于（无限阶）差分算子，我们称之为伯努利算子的性质。对于这类级数，我们证明了概率重整化与解析延拓是相容的。证明了$s\neq 1$的广义zeta级数是强重整化的，其重整化值由黎曼ζ函数给出.
英文摘要：
We introduce a theory of probabilistic renormalization for series, the renormalized values being encoded in the expectation of a certain random variable on the set of natural numbers. We identify a large class of weakly renormalizable series of Dirichlet type, whose analysis depends on the properties of a (infinite order) difference operator that we call Bernoulli operator. For the series in this class, we show that the probabilistic renormalization is compatible with analytic continuation. The general zeta series for $s\neq 1$ is found to be strongly renormalizable and its renormalized value is given by the Riemann zeta function.
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