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- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Mathematisches Seminar der Universität Hamburg and Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Algebra; Differential Geometry; Combinatorics; Number Theory; Topology; Geometry
- ISSN
- 0025-5858
- eISSN
- 1865-8784
- DOI
- 10.1007/s12188-014-0093-7
- Publisher site
- See Article on Publisher Site
Abstract
Given any complex number $$a$$ a , we prove that there are infinitely many simple roots of the equation $$\zeta (s)=a$$ ζ ( s ) = a with arbitrarily large imaginary part. Besides, we give a heuristic interpretation of a certain regularity of the graph of the curve $$t\mapsto \zeta ({1\over 2}+it)$$ t ↦ ζ ( 1 2 + i t ) . Moreover, we show that the curve $$\mathbb {R}\ni t\mapsto (\zeta ({1\over 2}+it),\zeta '({1\over 2}+it))$$ R ∋ t ↦ ( ζ ( 1 2 + i t ) , ζ ′ ( 1 2 + i t ) ) is not dense in $$\mathbb {C}^2$$ C 2 .
Journal
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Apr 15, 2014