On Kronecker limit formulas for real quadratic fields

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• 作者：Shuji Yamamoto
• 关键词：Zeta and L-functions ; Real quadratic fields ; Kronecker limit formula ; Double sine functions
• 刊名：Journal of Number Theory
• 出版年：2008
• 出版时间：February 2008
• 年：2008
• 卷：128
• 期：2
• 页码：426-450
• 全文大小：221 K

文摘

Let be the partial zeta function attached to a ray class 723111b4005f6917cac01a6e1c32d7""> 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 , which is related to , when we change the signature of .