A-points of the Riemann zeta-function on the critical line
2406 - 2436
International Mathematics Research Notices
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© 2014 © The Author(s) 2014. Published by Oxford University Press. All rights reserved. We investigate the proportion of the nontrivial roots of the equation ζ(s)=a, which lie on the line Rs= 1/2 for a in C not equal to zero. We show that at most one-half of these points lie on the line R s= 1/2. Moreover, assuming a spacing condition on the ordinates of zeros of the Riemann zeta-function, we prove that zero percent of the nontrivial solutions to ζ(s)=a lie on the line Rs= 1/2 for any nonzero complex number a.
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