On the zeros of \(\zeta(s)-c\) (Q365968)

For the Riemann zeta-function \(\zeta(s)\), the authors study the behavior of paths of zeros of \(\zeta(s)-c=0\), with \(c\in [0,1)\) by finding new zero-free regions for the functions \(\zeta(s)-c\). One can see that the zeros of \(\zeta(s)-c\) belong on the lines for which \(\text{Im}(\zeta(s))= 0\).NEWLINENEWLINEThe authors present an account of some results about these lines followed by the derivation of the zero-free regions for \(\zeta(s)-c\) on the right half-plane and the vertical boundary for the zeros of \(\zeta(s)-1\), where \(\mathrm{Re}(s)={1\over 2}\).