Computation of Weng's rank 2 zeta function over an algebraic number field☆
Computation of Weng's rank 2 zeta function over an algebraic number field☆
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代数数域上翁氏2阶zeta函数的计算☆
DOI：
10.1016/j.jnt.2006.12.007
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发表时间：
2007
影响因子：
0.7
通讯作者：
Tsukasa Hayashi
中科院分区：
文献类型：
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作者：
Tsukasa Hayashi
本文研究了由林翁提出的非阿贝尔zeta函数。我们可以将代数数域F的Weng的秩r ζ函数表示为秩为r的半稳定of格的模空间上的爱森斯坦级数的积分。对于r=2，在F=Q的情况下，Weng证明了它可以用Riemann ζ函数表示，Lagarias和Suzuki证明了它满足Riemann假设。这些结果由作者推广到虚二次域，由林翁推广到一般数域。本文给出了这两个结果的证明。推导了一般数域的2阶zeta函数的一个公式（由Weng首先发现），并证明了此类zeta函数的黎曼假设成立。
In this paper, we study the zeta function, named non-abelian zeta function, defined by Lin Weng. We can represent Weng's rank r zeta function of an algebraic number field F as the integration of the Eisenstein series over the moduli space of the semi-stable OF-lattices with rank r. For r=2, in the case of F=Q, Weng proved that it can be written by the Riemann zeta function, and Lagarias and Suzuki proved that it satisfies the Riemann hypothesis. These results were generalized by the author to imaginary quadratic fields and by Lin Weng to general number fields. This paper presents proofs of both these results. It derives a formula (first found by Weng) for Weng's rank 2 zeta functions for general number fields, and then proves the Riemann hypothesis holds for such zeta functions.
二级 zeta 及其零点
DOI：
--
发表时间：
2006
期刊：
J. Ramanujan Math. Soc. 21
影响因子：
--
作者：
木村素子;高野聡子;岡典子;Lin Weng
通讯作者：
Lin Weng