Lower estimates in the “large sieve”

Several Generalizations of Weil Sums

“…A number of incomplete character sum inequalities are given and further conjectures are formulated. Many of these inequalities have a combinatorial flavor since they are motivated by problems in graph theory [10,13,14] with applications to a number of areas in computer science [7,8,15,29,33,34].…”

“…Theorem 3.1, 3.4 and 3.6 give upper bounds for the r-discrepancies of a k-graph. There are a number of related applications such as amplifying random bits [15,29], communication complexity [7] and circuit complexity [20,21]. Conjecture 3.5, if true, would have significant consequence to k-party communication complexity.…”

On the Distribution of Powers in Finite Fields

“…To obtain the result in the F N case Burde [2] used orthogonality relations of CN instead of CN>. In this special case the theorem was independently proved by Sokolowskii [8].…”