[ Glen's Home ] [ VIU Math ] [ VIU Home ] [ email me ]

# Zeta Function Plotter

The applet below animates for real, where is the Riemann Zeta Function. See below for some tips on using the applet controls.

 Sorry, but the applet doesn't want to run for some reason

For , is defined as

where the series converges absolutely and uniformly, and is related to the prime numbers via the Euler product formula

Although fails to converge for , can be continued analytically to the entire complex plane except for where the zeta function has a simple pole. The famous Riemann Hypothesis is that all zeros of this function lie on the line where (called the critical line). It is known that there are infinitely many zeros located on the line. Zeros on this line occur where the little square in the animation passes through the coordinate.

The applet uses the Riemann-Siegel formula for computing values of the zeta function. Hopefully the applet controls are more or less obvious; pass the mouse over the various buttons for a short explanation in the messages'' area about their function. The current and value are shown in the upper left hand corner of the applet. Here a few tips:
• The trace button T'' will produce a nice trace of the path followed by the plot as increases. Click it again to clear the current trace.