Departmental Colloquium
Chantal David
Concordia University
The distribution of Gauss sums
Abstract: Gauss sums are fundamental objects in number theory. Quadratic Gauss sums
were studied by Gauss, and after many attempts, Gauss gave a simple
formula depending only on the argument of the Gauss sums modulo 4. Higher
degree Gauss sums seem to behave differently. Based on numerical
evidence, it was suggested by Kummer (1846) that the angles of cubic
Gauss at prime arguments are not equidistributed, and exhibit a bias
towards positive values. More extensive numerical testings seemed to
indicate that the bias does not persist, and that cubic Gauss sums are
indeed equidistributed, which was proven by Heath-Brown and Patterson
(1979). We will explain in this talk what is involved in proving
equidistribution of cubic Gauss sums, in particular why it took more
than 130 years after Kummer’s observations.
The talk will be accessible to a general mathematical audience, including
graduate students.
Friday February 9, 2024 at 3:00 PM in 636 SEO