scholarly journals Some mixed character sum identities of Katz

2017 ◽  
Vol 179 ◽  
pp. 17-32 ◽  
Author(s):  
Ron Evans
Keyword(s):  
Character Sum

scholarly journals ON SOLUTIONS TO SOME POLYNOMIAL CONGRUENCES IN SMALL BOXES

2013 ◽  
Vol 89 (2) ◽  
pp. 300-307
Author(s):  
IGOR E. SHPARLINSKI
Keyword(s):  
Exponential Sums ◽  
Polynomial Systems ◽  
Side Length ◽  
Character Sum ◽  
Number Of Solutions ◽  
Polynomial Congruences

AbstractWe use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime $p$. In particular, we obtain nontrivial results about the number of solutions in boxes with the side length below ${p}^{1/ 2} $, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.

scholarly journals Evaluation of a cubic character sum using the √−19 division points of the curve Y2 = X3 − 23 · 19X + 2 · 192

1984 ◽  
Vol 19 (2) ◽  
pp. 184-194 ◽  
Author(s):  
Dharam Bir Rishi ◽  
J.C. Parnami ◽  
A.R. Rajwade
Keyword(s):  
Character Sum

scholarly journals Stratification for Multiplicative Character Sums

2018 ◽  
Vol 2020 (10) ◽  
pp. 2881-2917 ◽  
Author(s):  
Junyan Xu
Keyword(s):  
Parameter Space ◽  
Rational Functions ◽  
Character Sums ◽  
Character Sum ◽  
Maximum Weight ◽  
Joint Work ◽  
Multiplicative Character ◽  
Multiplicative Characters ◽  
Sums Of Products ◽  
Multiplicative Character Sums

Abstract We prove a stratification result for certain families of n-dimensional (complete algebraic) multiplicative character sums. The character sums we consider are sums of products of r multiplicative characters evaluated at rational functions, and the families (with nr parameters) are obtained by allowing each of the r rational functions to be replaced by an “offset”, that is, a translate, of itself. For very general such families, we show that the stratum of the parameter space on which the character sum has maximum weight $n+j$ has codimension at least j⌊(r − 1)/2(n − 1)⌋ for 1 ≤ j ≤ n − 1 and ⌈nr/2⌉ for j = n. This result is used to obtain multivariate Burgess bounds in joint work with Lillian Pierce.

A multiple character sum evaluation

2005 ◽  
Vol 72 (1) ◽  
pp. 157-160
Author(s):  
Dae San Kim
Keyword(s):  
Character Sum ◽  
Möbius Inversion ◽  
Special Case ◽  
Multiple Character

We evaluate in a simple and direct manner a multiple character sum. a special case of which can also be derived from the Möbius inversion and a result of Hanlon.

scholarly journals A Problem Concerning a Character Sum

1999 ◽  
Vol 8 (1) ◽  
pp. 63-72 ◽  
Author(s):  
Edlyn Teske ◽  
Hugh C. Williams
Keyword(s):  
Character Sum

On a Congruence Related to Character Sums

1985 ◽  
Vol 28 (4) ◽  
pp. 431-439 ◽  
Author(s):  
J. H. H. Chalk
Keyword(s):  
Prime Power ◽  
Dirichlet Character ◽  
Character Sums ◽  
Arithmetic Progressions ◽  
Solution Set ◽  
Character Sum ◽  
Equal Degree

AbstractIf χ is a Dirichlet character to a prime-power modulus pα, then the problem of estimating an incomplete character sum of the form ∑1≤x≤h χ (x) by the method of D. A. Burgess leads to a consideration of congruences of the typef(x)g'(x) - f'(x)g(x) ≡ 0(pα),where fg(x) ≢ 0(p) and f, g are monic polynomials of equal degree with coefficients in Ζ. Here, a characterization of the solution-set for cubics is given in terms of explicit arithmetic progressions.

scholarly journals Some Identities on the Character Sum Containing x(x - 1)(x - λ)

1971 ◽  
Vol 42 ◽  
pp. 109-113 ◽  
Author(s):  
Masatoshi Yamauchi
Keyword(s):  
Character Sum ◽  
Legendre Symbol ◽  
Prime Field

Let Fp be the prime field of characteristic p (p: an odd prime), and put = Fp - {0, 1}. Then for λ ∈ we define,where denotes the Legendre symbol, and consider the sum

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