In this paper, we propose a tempered xi function obtained by the recombination of the decomposable functions for the Riemann xi function for the first time. We first obtain its functional equation and series representation. We then suggest three equivalent open problems for the zeros for it. We finally consider its behaviors on the critical line.

中文翻译：

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与黎曼 Xi 函数相关的缓和 Xi 函数

在本文中，我们首次提出了通过对黎曼 xi 函数的可分解函数重新组合而获得的调和 xi 函数。我们首先得到它的函数方程和级数表示。然后我们建议三个等效的开放问题来解决它的零点。我们最终考虑它在临界线上的行为。