منابع مشابه
Several generalizations of Weil sums
We consider several generalizations and variations of the character sum inequalities of Weil and Burgess. A number of incomplete character sum inequalities are proved while further conjectures are formulated. These inequalities are motivated by extremal graph theory with applications to problems in computer science.
متن کاملDivisibility of Weil Sums of Binomials
Consider the Weil sumWF,d(u) = ∑ x∈F ψ(x +ux), where F is a finite field of characteristic p, ψ is the canonical additive character of F , d is coprime to |F |, and u ∈ F . We say that WF,d(u) is threevalued when it assumes precisely three distinct values as u runs through F : this is the minimum number of distinct values in the nondegenerate case, and three-valuedWF,d are rare and desirable. W...
متن کاملCyclotomy of Weil Sums of Binomials
The Weil sum WK,d(a) = ∑ x∈K ψ(x d + ax) where K is a finite field, ψ is an additive character of K, d is coprime to |K|, and a ∈ K arises often in number-theoretic calculations, and in applications to finite geometry, cryptography, digital sequence design, and coding theory. Researchers are especially interested in the case where WK,d(a) assumes three distinct values as a runs through K. A Gal...
متن کاملQuasi-sums in Several Variables
In this note we introduce the notions of quasi-sums and of the local quasi-sums in several variables, respectively. We prove that the local quasi-sums are also quasi-sums. We show how this result can be applied to find the continuous solutions of the functional equation g(u11 + · · ·+ u1N , . . . , uM1 + · · ·+ uMN ) = f(g1(u11, . . . , uM1), . . . , gN (u1N , . . . , uMN )) that are strictly m...
متن کاملMultiple Harmonic Sums I: Generalizations of Wolstenholme’s Theorem
for complex variables s1, . . . , sl satisfying Re(sj) + · · · + Re(sl) > l − j + 1 for all j = 1, . . . , l. We call |s| = s1 + · · · + sl the weight and denote the length by l(s). The special values of multiple zeta functions at positive integers have significant arithmetic and algebraic meanings, whose defining series (1) will be called MZV series, including the divergent ones like ζ(. . . ,...
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: Journal of Number Theory
سال: 1994
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1084