Selfintersections of the Riemann zeta function on the critical line
Abstract
We show that the Riemann zeta function \zeta\ has only countably many selfintersections on the critical line, i.e., for all but countably many z in C the equation \zeta(1/2+it)=z has at most one solution t in 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) in R^2:a \ne b and F(a)=F(b)} is countable, or the image F(R) is a loop in C.
 Publication:

arXiv eprints
 Pub Date:
 October 2012
 arXiv:
 arXiv:1211.0044
 Bibcode:
 2012arXiv1211.0044B
 Keywords:

 Mathematics  Number Theory;
 11M06