Three-four-one inequality for Euler products
= Three-four-one inequality for Euler products
For every complex number $z$ with $|z|\leq1$,
$$
3+4\Re z+\Re(z^2)\geq0.
$$
Applying this to each prime-power term in logarithms of Euler products proves that
$$
\zeta(\sigma)^3|D_f(\sigma+it)|^4|D_{f^2}(\sigma+2it)|\geq1
$$
for $\sigma>1$ and every completely multiplicative $f$ bounded by one.