
Anthony Henderson
University of Sydney
Fourier transform and Kloosterman sums.
Friday 18th October, 121pm,
Carslaw 373.
Fourier transform on vector spaces over a finite field
is defined as over the reals, using a sum instead of an integral.
An interesting application of it was discovered by Springer:
if your vector space is the dual of a Lie algebra, and you take
the Fourier transform of the indicator function of a strongly
regular coadjoint orbit, the result has a lot in common with the
generic characters of the corresponding group. I will give an
easy introduction to this idea, and suggest how a similar procedure
might help in computing certain trigonometric sums which generalize
Kloosterman sums.







