کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616640 1339355 2013 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Self-intersections of the Riemann zeta function on the critical line
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Self-intersections of the Riemann zeta function on the critical line
چکیده انگلیسی

We show that the Riemann zeta function ζζ has only countably many self-intersections on the critical line, i.e., for all but countably many z∈Cz∈C the equation ζ(12+it)=z has at most one solution t∈Rt∈R. More generally, we prove that if FF is analytic in a complex neighborhood of RR and locally injective on RR, then either the set {(a,b)∈R2:a≠b  and  F(a)=F(b)}{(a,b)∈R2:a≠b  and  F(a)=F(b)} is countable, or the image F(R)F(R) is a loop in CC.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 406, Issue 2, 15 October 2013, Pages 475–481
نویسندگان
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