The page reproduced above is from Gauss,
and concerns what we now call Gauss sums,
which crop up often in my work.
Daniel J. KatzAssistant Professor
Department of Mathematics
California State University, Northridge
I investigate problems in number theory and discrete
mathematics, often motivated by information theory.
Both algebra and analysis play crucial roles.
Some of my recent work includes a proof for finite fields
of characteristic 2 and 3 of a conjecture of Helleseth (1976)
concerning cross-correlations of maximal linear recursive
sequences (equivalent to a conjecture about Weil sums of
binomials or a statement about weights in certain error-
In a similar area, Philippe Langevin and I proved a conjecture
of Dobbertin, Helleseth, Kumar, and Martinsen (2001) that
asserts the existence of an infinite a three-valued family of
Weil sums of binomials. This is the tenth infinite family
discovered since 1966.
Jonathan Jedwab, Kai-Uwe Schmidt, and I have settled con-
jectures of Høholdt-Jensen (1988), Borwein-Choi-Jedwab (2004),
Parker (2005), Yu-Gong (2007), and Jedwab-Schmidt (2010) on
the asymptotic L4 norm of certain families of Littlewood
polynomials. In doing so, we break a record (which stood for
over two decades) for the lowest known asymptotic mean-square
autocorrelation for binary sequences.