All but Finitely Many Non‐Trivial Zeros of the Approximations of the Epstein Zeta Function are Simple and on the Critical Line
All but Finitely Many Non‐Trivial Zeros of the Approximations of the Epstein Zeta Function are Simple and on the Critical Line
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Epstein Zeta 函数逼近的所有非平凡零点都是简单的且位于临界线上
DOI：
10.1112/s0024611504015060
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发表时间：
2005
影响因子：
1.8
通讯作者：
Haseo Ki
中科院分区：
文献类型：
--
作者：
Haseo Ki
Chowla-Selberg公式用于逼近给定的Epstein zeta函数。该系列的部分和源自Chowla-Selberg公式，尽管这些部分和满足函数方程（就像Epstein zeta函数一样），但它们不具有欧拉积。我们在本文中所称的部分和可以被认为是关于一个更一般的函数只满足一个函数方程的特殊情况。本文研究了函数零点的分布。我们表明，在任何带包含的临界线，所有的，但1000多个零点的功能是简单的，在临界线上。对于许多Epstein zeta函数，我们证明了Chowla-Selberg公式中部分和的所有非平凡零点都是简单的，并且在临界线上。2000年数学学科分类11 M26。
The Chowla–Selberg formula is applied in approximating a given Epstein zeta function. Partial sums of the series derive from the Chowla–Selberg formula, and although these partial sums satisfy a functional equation, as does an Epstein zeta function, they do not possess an Euler product. What we call partial sums throughout this paper may be considered as special cases concerning a more general function satisfying a functional equation only. In this article we study the distribution of zeros of the function. We show that in any strip containing the critical line, all but finitely many zeros of the function are simple and on the critical line. For many Epstein zeta functions we show that all but finitely many non‐trivial zeros of partial sums in the Chowla–Selberg formula are simple and on the critical line. 2000 Mathematics Subject Classification 11M26.