On certain ray class invariants of real quadratic fields
On certain ray class invariants of real quadratic fields
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关于实二次场的某些射线类不变量
DOI：
10.2969/jmsj/03010139
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发表时间：
1977
影响因子：
0.7
通讯作者：
T. Shintani
中科院分区：
文献类型：
--
作者：
T. Shintani
0 - 1。H. M. Stark在[10]，[11]和[12]三篇论文中，利用全实场的l -级数的导数在s=0处的值，引入了全实场的射线类不变量。然后，他提出了一个关于不变量的算术性质的惊人猜想（用数值证据）。在本文中，我们证明了对于给定的实二次域，不变量是用一个特殊函数的特殊值来描述的。该函数与E. W. Barnes的双伽马函数密切相关。然后我们证明了一个非常特殊（但非平凡）的情况下的猜想。
0-1. In his papers [10], [11] and [12], H. M. Stark introduced certain ray class invariants for totally real fields in terms of the value at s=0 of the derivative of some L-series of the fields. Then he presented (with numerical evidences) a striking conjecture on the arithmetic nature of the invariants. In this paper, we show that, for each given real quadratic field, the invariants are described in terms of special values of a certain special function. The function is closely related to the double gamma function of E. W. Barnes. Then we prove the conjecture for a very special (but non-trivial) case.