## Riemann-Siegel Functions

For a Real Positive , the Riemann-Siegel function is defined by

The top plot superposes (thick line) on , where is the Riemann Zeta Function.

The Riemann-Siegel theta function appearing above is defined by

These functions are implemented in Mathematica
(Wolfram Research, Champaign, IL) as RiemannSiegelZ[z] and RiemannSiegelTheta[z], illustrated above.