Xi modulus criterion for the Riemann hypothesis
= Xi modulus criterion for the Riemann hypothesis
<Riemann hypothesis> is equivalent to monotonicity of $\sigma\mapsto|\xi(\sigma+it)|$ for every fixed $t$ on $\sigma\ge1/2$. Under <Riemann hypothesis> the <real logarithmic derivative of Riemann xi> is positive for $\sigma>1/2$. Conversely a zero right of that line would force the nonnegative monotone modulus to vanish on an interval, contrary to the <identity theorem>. Functional symmetry rules out zeros to the left.