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.See also Riemann Zeta Function
References
Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 143, 1991.
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