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An estimate of incomplete multiplicative character sum of polynomials
Discrete Mathematics and Applications, 1992See the review in Zbl 0712.11051.
Stepanov, S. A., Shparlinskij, I. E.
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Lower estimates of sums of polynomial characters
Mathematical Notes of the Academy of Sciences of the USSR, 1973An 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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Estimates for character sums in number fields
Israel Journal of Mathematics, 1987Let \(\rho_ 1,...,\rho_ r\) 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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A METHOD FOR ESTIMATING DOUBLE SUMS WITH REAL QUADRATIC CHARACTER, AND APPLICATIONS
Mathematics of the USSR-Izvestiya, 1971In 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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An Estimate of Incomplete Mixed Character Sums
2010Dedicated 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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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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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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A lower bound estimate for complete sums of characters of polynomials and rational functions
Acta Mathematica Sinica, 1993The paper deals with complete Dirichlet character sums of type \[ S_ k(\chi,q)=\sum^ q_{\ell=1}{}' \chi(a\ell^ k+b) \qquad\text{or}\qquad T_ k(\chi,q)=\sum^ q_{\ell=1}{}' \chi((a\ell^ k+b)/(c\ell^ k+d)), \] where \(\chi\) denotes a primitive character \(\bmod q\).
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Moscow University Mathematics Bulletin, 2008
Estimates of short sums of Dirichlet characters over shifted prime numbers are obtained in the case when the modulus of a character is a power of a fixed prime number.
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Estimates of short sums of Dirichlet characters over shifted prime numbers are obtained in the case when the modulus of a character is a power of a fixed prime number.
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The Mean Values of Character Sums and Their Applications
Mathematics, 2021Jiafan Zhang, Yuanyuan Meng
exaly