Interactive Supplement to the paper
The dynamical motion of the zeros of the partial sums of
ez, and its relationship to discrepancy theory
The page presents an interactive graphical illustration of the results
in the paper. The interactive supplement appears in the figure below.
A Java-enabled web browser is required to view and interact with the
The figure displays the zeros of the partial sums
for 1≤n≤200 and comptues the associated discrepancy
function values for a given sector. The value of n and
the sector can be selected interactively.
Richard S. Varga, Amos J. Carpenter, and Bryan W. Lewis
Electronic Transactions on Numerical Analysis, Vol. 30 (2008),
The figure consist of three parts:
- The large plot displays the zeros of
sn(nz) for the selected value of n,
the Szegő curve, the selected sector, and a brief statement listing the
value of n (the degree), the sector angle,
a count of the number of zeros of
falling in the sector, and a computed value of the discrepancy
function for the given data. The zeros appear as small blue crosses; the
Szegő curve appears as a red curve. The selected sector is shaded.
- A set of controls for selecting the value of n and a button to clear the
"history" plot of discrepancy function values appears just below the main plot.
- The small plot at the bottom displays up to the most recent 100 computed
discrepancy function values.
The zeros of
sn(nz) for each value of n from
1 to 200 were computed a priori with extended-precision arithmetic, and stored
as Java double precision floating point numbers with approximately
16 decimal digits of accuracy.
All computations are performed by the client Java virtual machine using
The displayed computed values of the
discrepancy function are rounded to four decimal digits. Note that the
accuracy of the plot data is limited to the pixel display resolution of
about 500x500 pixels. The display resolution affects the ability to
select sector angles and may slightly affect the display of the zeros.