Various algebraic properties of Heilbronn's exponential sum can be deduced through the
use of supercharacter theory, a novel extension of classical character theory due to Diaconis …

We consider families of exponential sums indexed by a subgroup of invertible classes
modulo some prime power q. For fixed d, we restrict to moduli q so that there is a unique …

We use supercharacter theory to study moments of Gaussian periods. For $ p-1= dk $ and
fixed $ k $, we compute the fourth absolute moments for all but finitely many primes $ p …

Recent work has introduced the study of graphical properties of cyclic supercharacters,
functions $\mathbb {Z}/n\mathbb {Z}\to\mathbb {C} $ whose values are exponential sums …

In recent work, R. Moerman and H. Weigert have introduced a truncation scheme for the
Balitsky hierarchy, arguing that this is the most general possible method for obtaining finite …

Exponential sums are sums of roots of unity which can be defined in a very elementary way.
As sums of complex numbers of absolute value 1, they can always be trivially bounded by …

We explore the thought processes, strategies, and pitfalls involved in entering new territory,
developing novel projects, and seeing them through to publication. We propose twenty-one …