کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595030 1335794 2008 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Kronecker limit formulas for real quadratic fields
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On Kronecker limit formulas for real quadratic fields
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 128, Issue 2, February 2008, Pages 426-450