کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4594110 1335740 2013 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Explicit upper bounds for the Stieltjes constants
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Explicit upper bounds for the Stieltjes constants
چکیده انگلیسی

TextLet χ be a primitive Dirichlet character modulo q   and let (−1)nγn(χ)/n!(−1)nγn(χ)/n! (for n larger than 0) be the n  -th Laurent coefficient around z=1z=1 of the associated Dirichlet L-series. When χ   is non-principal, (−1)nγn(χ)(−1)nγn(χ) is simply the value of the n  -th derivative of L(z,χ)L(z,χ) at z=1z=1. In this paper we give an explicit upper bounds for |γn(χ)||γn(χ)| for q⩽π2e(n+1)/2n+1. In particular, when q=1q=1 the explicit upper bound we get improves on earlier work. We conclude this paper by showing that we can altogether dispense in these proofs with the functional equation of L(z,χ)L(z,χ).VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=q340UciEvAA.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 133, Issue 3, March 2013, Pages 1027–1044
نویسندگان
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