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