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arXiv · 1011.5339

On the roots of the equation $\zeta(s)=a$

R. Garunkstis·J. Steuding
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Abstract

Given any complex number $a$, we prove that there are infinitely many simple roots of the equation $\zeta(s)=a$ with arbitrarily large imaginary part. Besides, we give a heuristic interpretation of a certain regularity of the graph of the curve $t\mapsto \zeta({1\over 2}+it)$. Moreover, we show that the curve $t\mapsto (\zeta({1\over 2}+it),\zeta'({1\over 2}+it))$ is not dense in $C^2$.

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BibTeXRIS

R. Garunkstis, J. Steuding. 2010-11-24. On the roots of the equation $\zeta(s)=a$. https://doi.org/10.1007/s12188-014-0093-7

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