scholarly journals Ax’s theorem with an additive character

2021 ◽  
Vol 8 (1) ◽  
pp. 179-216
Author(s):  
Ehud Hrushovski
Keyword(s):  
Additive Character

GOWERS UNIFORMITY NORM AND PSEUDORANDOM MEASURES OF THE PSEUDORANDOM BINARY SEQUENCES

2011 ◽  
Vol 07 (05) ◽  
pp. 1279-1302 ◽  
Author(s):  
HUANING LIU
Keyword(s):  
Exponential Sums ◽  
Binary Sequences ◽  
Vandermonde Determinant ◽  
Additive Character ◽  
Pseudorandom Sequences ◽  
Multiplicative Inverse ◽  
Large Families ◽  
Points Of View ◽  
Pseudorandom Measures ◽  
Gowers Norm

Recently there has been much progress in the study of arithmetic progressions. An important tool in these developments is the Gowers uniformity norm. In this paper we study the Gowers norm for pseudorandom binary sequences, and establish some connections between these two subjects. Some examples are given to show that the "good" pseudorandom sequences have small Gowers norm. Furthermore, we introduce two large families of pseudorandom binary sequences constructed by the multiplicative inverse and additive character, and study the pseudorandom measures and the Gowers norm of these sequences by using the estimates of exponential sums and properties of the Vandermonde determinant. Our constructions are superior to the previous ones from some points of view.

ON THREE-VARIABLE EXPANDERS OVER FINITE FIELDS

2014 ◽  
Vol 10 (03) ◽  
pp. 689-703 ◽  
Author(s):  
LE ANH VINH
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Alternative Proof ◽  
Character Sum ◽  
Additive Character ◽  
Product Graphs

Let 𝔽q be the finite field with q elements and P(x, y) be a polynomial in 𝔽q[x, y]. Using additive character sum estimates, we study expander property of the function x1 + P(x2, x3). We give an alternative proof using spectra of sum–product graphs in the case of P(x, y) = xy, and also extend the problem in the setting of finite cyclic rings.

Bilinear character sums and sum-product problems on elliptic curves

2010 ◽  
Vol 53 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Omran Ahmadi ◽  
Igor Shparlinski
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Character Sums ◽  
Multiplicative Character ◽  
Additive Character ◽  
Product Problem ◽  
Multiplicative Character Sums

AbstractLet E be an ordinary elliptic curve over a finite field q of q elements. We improve a bound on bilinear additive character sums over points on E, and obtain its analogue for bilinear multiplicative character sums. We apply these bounds to some variants of the sum-product problem on E.

Large family of pseudorandom subsets of the set of the integers not exceeding N

2014 ◽  
Vol 10 (05) ◽  
pp. 1121-1141 ◽  
Author(s):  
Huaning Liu
Keyword(s):  
Large Family ◽  
Additive Character ◽  
Multiplicative Inverse ◽  
The Family ◽  
Large Families ◽  
Pseudorandom Measures

In a series of papers, Dartyge and Sárközy (partly with other coauthors) studied large families of pseudorandom subsets. In this paper, we introduce a new large family of pseudorandom subsets constructed by the multiplicative inverse and additive character, and study the pseudorandom measures. Furthermore, we extend the family of subsets to the case when the moduli is composite.

scholarly journals Roman Model-Books as a Resource for Digital Architectural Reconstructions

Heritage ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 20-32
Author(s):  
Josef Souček
Keyword(s):  
Computer Game ◽  
Visual Language ◽  
Additive Character ◽  
Roman Painting ◽  
Virtual Landscapes ◽  
Level Design ◽  
Roman Model

Upon examination of Roman landscape paintings preserved in situ and in museums of Naples and Rome, additional evidence has been found for the additive character of creation of imaginary landscapes as well as evidence for using standardized elements and whole scene compositions in Roman painting. This attitude is compared to the modern way of creating virtual landscapes—computer game level design and the process called “kitbashing”. I propose that both these processes share the same task to create a familiar landscape using a visual language understandable to its contemporary viewer, but also a very similar method of using predefined elements.

Additive character of the resonance constants of azinyl groups

1989 ◽  
Vol 25 (3) ◽  
pp. 296-300
Author(s):  
O. P. Shkurko ◽  
V. P. Mamaev
Keyword(s):  
Additive Character
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