Record number :
1563800
Title of article :
Self-intersections of the Riemann zeta function on the critical line
Author/Authors :
Banks، نويسنده , , William and Castillo-Garate، نويسنده , , Victor and Fontana، نويسنده , , Luigi and Morpurgo، نويسنده , , Carlo، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2013
Pages :
7
From page :
475
To page :
481
Abstract :
We show that the Riemann zeta function ζ has only countably many self-intersections on the critical line, i.e., for all but countably many z ∈ C the equation ζ ( 1 2 + i t ) = z has at most one solution t ∈ R . More generally, we prove that if F is analytic in a complex neighborhood of R and locally injective on R , then either the set { ( a , b ) ∈ R 2 : a ≠ b  and  F ( a ) = F ( b ) } is countable, or the image F ( R ) is a loop in C .
Keywords :
Self-intersections , Riemann zeta function , Critical line
Journal title :
Journal of Mathematical Analysis and Applications
Serial Year :
2013
Link To Document :
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