On Kronecker limit formulas for real quadratic fields
On Kronecker limit formulas for real quadratic fields
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实二次域的克罗内克极限公式
DOI：
10.1016/j.jnt.2007.05.010
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发表时间：
2006
影响因子：
0.7
通讯作者：
Shuji Yamamoto
中科院分区：
文献类型：
--
作者：
Shuji Yamamoto
设ε（s，C）是真实的二次域的射线类C上的偏zeta函数.结合Zagier和Shintani的一些思想和方法，我们研究了s=1和s=0时的zeta函数。主要结果是：（1）推广了Zagier关于s=1时Laurent展开式常数项的公式;（2）给出了与连分式理论有关的s=0时的值和一阶导数的表达式;（3）简单描述了当改变C的签名时，与λ ′（0，C）有关的Shintani不变量X（C）的行为.
Let ζ(s,C) be the partial zeta function attached to a ray class C of a real quadratic field. We study this zeta function at s=1 and s=0, combining some ideas and methods due to Zagier and Shintani. The main results are (1) a generalization of Zagier's formula for the constant term of the Laurent expansion at s=1, (2) some expressions for the value and the first derivative at s=0, related to the theory of continued fractions, and (3) a simple description of the behavior of Shintani's invariant X(C), which is related to ζ′(0,C), when we change the signature of C.