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

(Wolfram Research, Champaign, IL) as

**References**

Vardi, I. *Computational Recreations in Mathematica.* Reading, MA: Addison-Wesley, p. 143, 1991.

© 1996-9

1999-05-25