Results 211 to 220 of about 67,818,891 (245)

Estimation of a Character Sum

Bulletin of the London Mathematical Society, 1988
The author estimates the sum \[ A=\sum_ ...
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Some Estimates for Character Sums and Applications

Designs, Codes and Cryptography, 2001
Let \(p\) be a prime number, \(F_{q}\) a finite field with \(q=p^{ \nu}\) elements, \(S\) a subset of \(F_{q}\), and \( \chi\) a nontrivial multiplicative character of the field \(F_{q}\) of order \(s \geq 2\). If \(n \geq 2\) is an arbitrary integer satisfying \(n \not\equiv 0\pmod s\), the author proves that there exists a monic irreducible ...
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The Character Sum Estimate with r = 3

Journal of the London Mathematical Society, 1986
This paper is the culmination of the author's recent efforts to extend his well-known character sum estimates to arbitrary moduli. He shows that for any non-principal character \(\chi\) modulo \(k\) and arbitrary positive integers \(N\) and \(H\) the estimate \[ \sum^{N+H}_{n=N+1}\chi (n) \ll_{\varepsilon} H^{1-(1/r)} k^{(r+1)/4r^ 2+\varepsilon}\tag{*}
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Estimation of Character Sums Modulo a Power of a Prime

Proceedings of the London Mathematical Society, 1986
Let \(\chi\) be a primitive character modulo \(k\), and let \[ S(N,H)=\sum_{n=N+1}^{N+H}\chi(n). \] The author's celebrated character sum estimate [ibid. 13, 524--536 (1963; Zbl 0123.04404)] states that the bound \[ S(N,H)\ll_{r,\varepsilon} H^{1-(1/r)} k^{(r+1)/4r^2+\varepsilon} \tag{*} \] holds uniformly in \(N\) and \(H\) for any \(\varepsilon >0 ...
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An estimate of incomplete multiplicative character sum of polynomials

Discrete Mathematics and Applications, 1992
See the review in Zbl 0712.11051.
Stepanov, S. A., Shparlinskij, I. E.
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Estimates for character sums in number fields

Israel Journal of Mathematics, 1987
Let \(\rho_ 1,...,\rho_ r\) be (continuous) complex finite-dimensional representations of the Weil group of an algebraic number field K of finite degree over the rationals. Let \[ L(s,\rho_ j)=\sum_{{\mathfrak a}}c({\mathfrak a},\rho_ j)(N{\mathfrak a})^{-s},\quad 1\leq j\leq r, \] be the Artin-Weil L-function associated to \(\rho_ j\).
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Lower estimates of sums of polynomial characters

Mathematical Notes of the Academy of Sciences of the USSR, 1973
An infinite sequence of primes p is formulated, and for each p polynomials of formaxn+b, (a, p)=(b, p)=1, are indicated such that $$\sum\nolimits_{x = 1}^p {\left( {\frac{{ax^n + b}}{p}} \right) = p,n \asymp \frac{p}{{log p}}.}$$
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An Estimate of Incomplete Mixed Character Sums

2010
Dedicated to Endre Szemeredi for his 70th birthday. In this note we consider incomplete mixed character sums over a finite field \( \mathbb{F}_{p^n } \) of the form \( \sum\nolimits_{x \in B_H } {\psi \left( {f\left( x \right)} \right)\chi \left( x \right)} \) where is an additive character, \( f\left( x \right) \in \mathbb{F}_{p^n } \) a polynomial, x
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A METHOD FOR ESTIMATING DOUBLE SUMS WITH REAL QUADRATIC CHARACTER, AND APPLICATIONS

Mathematics of the USSR-Izvestiya, 1971
In this paper we examine a general method for estimating double sums with real quadratic character and give some applications to the theory of quadratic forms and the theory of divisors of quadratic fields.
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Two Applications of an Incomplete Additive Character Sum to Estimating Nonlinearity of Boolean Functions

2011
In recent years, several classes of Boolean functions with good cryptographic properties have been constructed by using univariate (or bivariate) polynomial representation of Boolean functions over finite fields. The estimation of an incomplete additive character sum plays an important role in analyzing the nonlinearity of these functions.
Yusong Du, Fangguo Zhang
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