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Let $t$ represent the imaginary part of a zeta zero on the critical line. The asymptotic expansion of RiemannSiegelTheta[t] for large $t$ is Simplify[Series[RiemannSiegelTheta[t], {t, Infinity, 2}]] the first term of which is $\frac{1}{2}{\rm Log}[\frac{t}{2\pi}]-\frac{1}{2}$. For large $t$, the phase of the zeta function on the critical line is ...

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