bounds of Riemann $\zeta(s)$ function on the critical line? I vaguely remembered that 
$$0\leq|\zeta(1/2+i t)|\leq C t^{\epsilon},\qquad t>>1,\epsilon>0$$.
Is this bound correct?
Thanks-
mike

In: http://www.math.tifr.res.in/~publ/ln/tifr01.pdf  pp.97-99 , it is proven that:
$$\zeta(s) < A(d)t^{1-d},  \text{for } \sigma=\mathrm{Re}(s) \geq d,  0 < d < 1  ; t=\mathrm{Im}(s) \geq 1  .$$                 
with $A(d) = (1/(1-e) + 1 + 3/e)$.
