کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897008 | 1630628 | 2018 | 35 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Average values of L-functions in even characteristic
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let k=Fq(T) be the rational function field over a finite field Fq, where q is a power of 2. In this paper we solve the problem of averaging the quadratic L-functions L(s,Ïu) over fundamental discriminants. Any separable quadratic extension K of k is of the form K=k(xu), where xu is a zero of X2+X+u=0 for some uâk. We characterize the family I (resp. F, Fâ²) of rational functions uâk such that any separable quadratic extension K of k in which the infinite prime â=(1/T) of k ramifies (resp. splits, is inert) can be written as K=k(xu) with a unique uâI (resp. uâF, uâFâ²). For almost all sâC with Re(s)â¥12, we obtain the asymptotic formulas for the summation of L(s,Ïu) over all k(xu) with uâI, all k(xu) with uâF or all k(xu) with uâFâ² of given genus. As applications, we obtain the asymptotic mean value formulas of L-functions at s=12 and s=1 and the asymptotic mean value formulas of the class number hu or the class number times regulator huRu.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 186, May 2018, Pages 269-303
Journal: Journal of Number Theory - Volume 186, May 2018, Pages 269-303
نویسندگان
Sunghan Bae, Hwanyup Jung,