Bounds of Gauss sums in finite fields
نویسندگان
چکیده
منابع مشابه
Bounds of Gauss Sums in Finite Fields
We consider Gauss sums of the form Gn(a) = ∑ x∈Fpm χ(x) with a nontrivial additive character χ 6= χ0 of a finite field Fpm of pm elements of characteristic p. The classical bound |Gn(a)| ≤ (n−1)pm/2 becomes trivial for n ≥ pm/2 + 1. We show that, combining some recent bounds of HeathBrown and Konyagin with several bounds due to Deligne, Katz, and Li, one can obtain the bound on |Gn(a)| which is...
متن کاملPure Gauss Sums over Finite Fields
New classes of pairs e,p are presented for which the Gauss sums corresponding to characters of order e over finite fields of characteristic p are pure, i.e., have a real power. Certain pure Gauss sums are explicitly evaluated. §
متن کاملIndex bounds for character sums of polynomials over finite fields
Abstract. We provide an index bound for character sums of polynomials over finite fields. This improves the Weil bound for high degree polynomials with small indices, as well as polynomials with large indices that are generated by cyclotomic mappings of small indices. As an application, we also give some general bounds for numbers of solutions of some Artin-Schreier equations and mininum weight...
متن کاملCyclotomic-intermediate Fields via Gauss Sums
Let p be an odd prime, and let m divide p−1. Let ζ = e and let ω = e. The field extension Q(ω) ⊂ Q(ω, ζ) is Galois with cyclic Galois group isomorphic to (Z/pZ)×. The unique field between Q(ω) and Q(ω, ζ) having degree m over Q(ω) takes the form Q(ω, τ) where τ is a Gauss sum, to be described below. Furthermore, under some conditions we can compute τ as an element α of Q(ω), thus expressing the...
متن کاملCharacter Sums in Finite Fields
Let F q be a finite field of order q with q = p n , where p is a prime. A multiplicative character χ is a homomorphism from the multiplicative group F * q , ·· to the unit circle. In this note we will mostly give a survey of work on bounds for the character sum x χ(x) over a subset of F q. In Section 5 we give a nontrivial estimate of character sums over subspaces of finite fields. §1. Burgess'...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07133-3