On a Question of Davenport and Lewis and New Character Sum Bounds in Finite Fields

@inproceedings{Chang2007OnAQ,
  title={On a Question of Davenport and Lewis and New Character Sum Bounds in Finite Fields},
  author={Mei-Chu Chang},
  year={2007}
}
Let χ be a nontrivial multiplicative character of Fpn . We obtain the following results. (1). Let ε > 0 be given. If B = {nj=1 xjωj : xj ∈ [Nj +1, Nj +Hj ]∩Z, j = 1, . . . , n} is a box satisfying n Π j=1 Hj > p ( 5+ε)n, then for p > p(ε) and some absolute constant c > 0, we have, denoting χ a nontrivial multiplicative character | ∑ x∈B χ(x)| < cnp− ε 2 4 |B| unless n is even, χ is principal on a subfield F2 of size pn/2 and maxξ |B∩ξF2| > p−ε|B|. (2). Assume A, B ⊂ Fp such that |A| > p 9+ε, |B… CONTINUE READING