کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415700 1335766 2011 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the mean square average of special values of L-functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the mean square average of special values of L-functions
چکیده انگلیسی

Let χ be a Dirichlet character and L(s,χ) be its L-function. Using weighted averages of Gauss and Ramanujan sums, we find exact formulas involving Jordanʼs and Eulerʼs totient function for the mean square average of L(1,χ) when χ ranges over all odd characters modulo k and L(2,χ) when χ ranges over all even characters modulo k. In principle, using our method, it is always possible to find the mean square average of L(r,χ) if χ and r⩾1 have the same parity and χ ranges over all odd (or even) characters modulo k, though the required calculations become formidable when r⩾3. Consequently, we see that for almost all odd characters modulo k, |L(1,χ)|<Φ(k), where Φ(x) is any function monotonically tending to infinity.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 131, Issue 8, August 2011, Pages 1470-1485
نویسندگان
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