Character sums and arithmetic combinatorics

2016 ◽  
pp. 405-417
Author(s):  
Mei-Chu Chang
Keyword(s):  
Character Sums ◽  
Arithmetic Combinatorics

scholarly journals The Mean Values of Character Sums and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 318
Author(s):  
Jiafan Zhang ◽  
Yuanyuan Meng
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Mean Values ◽  
Special Polynomials ◽  
Elementary Methods ◽  
The Mean

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.

scholarly journals Equidistribution Among Cosets of Elliptic Curve Points in Intervals

2020 ◽  
Vol 14 (1) ◽  
pp. 339-345
Author(s):  
Taechan Kim ◽  
Mehdi Tibouchi
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Character Sums ◽  
Fault Analysis ◽  
Signature Schemes ◽  
Large Subgroup

AbstractIn a recent paper devoted to fault analysis of elliptic curve-based signature schemes, Takahashi et al. (TCHES 2018) described several attacks, one of which assumed an equidistribution property that can be informally stated as follows: given an elliptic curve E over 𝔽q in Weierstrass form and a large subgroup H ⊂ E(𝔽q) generated by G(xG, yG), the points in E(𝔽q) whose x-coordinates are obtained from xG by randomly flipping a fixed, sufficiently long substring of bits (and rejecting cases when the resulting value does not correspond to a point in E(𝔽q)) are close to uniformly distributed among the cosets modulo H. The goal of this note is to formally state, prove and quantify (a variant of) that property, and in particular establish sufficient bounds on the size of the subgroup and on the length of the substring of bits for it to hold. The proof relies on bounds for character sums on elliptic curves established by Kohel and Shparlinski (ANTS–IV).

scholarly journals On character sums in finite fields

1939 ◽  
Vol 71 (0) ◽  
pp. 99-121 ◽  
Author(s):  
H. Davenport
Keyword(s):  
Finite Fields ◽  
Character Sums

scholarly journals On the Mean Values of Certain Character Sums

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Zhefeng Xu ◽  
Huaning Liu
Keyword(s):  
Character Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Mean Values ◽  
Asymptotic Formulae ◽  
Fourth Power Mean ◽  
The Mean

Letq≥5be an odd number. In this paper, we study the fourth power mean of certain character sums∑χmodq,χ-1=-1*∑1≤a≤q/4aχa4and∑χmodq,χ-1=1*∑1≤a≤q/4aχa4, where∑‍*denotes the summation over primitive characters moduloq, and give some asymptotic formulae.

scholarly journals Estimates for Mixed Character Sums

2008 ◽  
Vol 18 (4) ◽  
pp. 1251-1269 ◽  
Author(s):  
Nicholas M. Katz
Keyword(s):  
Character Sums

Covering arrays from m-sequences and character sums

2016 ◽  
Vol 85 (3) ◽  
pp. 437-456 ◽  
Author(s):  
Georgios Tzanakis ◽  
Lucia Moura ◽  
Daniel Panario ◽  
Brett Stevens
Keyword(s):  
Character Sums ◽  
Covering Arrays ◽  
M Sequences

scholarly journals Legendre character sums

1992 ◽  
Vol 22 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Yoshiaki Sawabe
Keyword(s):  
Character Sums

scholarly journals Extended Bounds of Beatty Sequence Associated with Primes

2019 ◽  
Vol 8 (6S3) ◽  
pp. 115-118
Keyword(s):  
Character Sums ◽  
Beatty Sequences ◽  
Composite Moduli ◽  
Beatty Sequence

This paper discusses on the estimation of character sums with respect to non-homogeneous Beatty sequences, over prime where , and is irrational. In particular, the bounds is found by extending several properties of character sums associated with composite moduli over prime. As a result, the bound of is deduced.

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