scholarly journals Analogues of the Balog–Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions

2019 ◽  
Vol 23 (1) ◽  
pp. 183-205
Author(s):  
Oliver Roche-Newton ◽  
Igor E. Shparlinski ◽  
Arne Winterhof
Keyword(s):  
Finite Fields ◽  
Character Sums

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

Equations in finite fields with restricted solution sets. I (Character sums)

2007 ◽  
Vol 118 (1-2) ◽  
pp. 129-148 ◽  
Author(s):  
K. Gyarmati ◽  
A. Sárközy
Keyword(s):  
Finite Fields ◽  
Character Sums ◽  
Solution Sets

scholarly journals A note on character sums in finite fields

2017 ◽  
Vol 46 ◽  
pp. 247-254 ◽  
Author(s):  
Abhishek Bhowmick ◽  
Thái Hoàng Lê ◽  
Yu-Ru Liu
Keyword(s):  
Finite Fields ◽  
Character Sums

scholarly journals Solutions of equations over finite fields: Enumeration via bijections

2016 ◽  
Vol 15 (07) ◽  
pp. 1650136 ◽  
Author(s):  
Ioulia N. Baoulina
Keyword(s):  
Recent Result ◽  
Finite Fields ◽  
Simple Proof ◽  
Character Sums ◽  
Alternative Proof ◽  
Number Of Solutions ◽  
Combinatorial Argument ◽  
Solutions Of Equations

We present a simple proof of the well-known fact concerning the number of solutions of diagonal equations over finite fields. In a similar manner, we give an alternative proof of the recent result on generalizations of Carlitz equations. In both cases, the use of character sums is avoided by using an elementary combinatorial argument.

scholarly journals ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS

2008 ◽  
Vol 50 (3) ◽  
pp. 523-529 ◽  
Author(s):  
IGOR E. SHPARLINSKI
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Absolute Constant ◽  
Character Sums ◽  
Multiplicative Character ◽  
Image Position ◽  
Multiplicative Character Sums ◽  
Bilinear Equations

AbstractWe consider the equation over a finite field q of q elements, with variables from arbitrary sets $\cA,\cB, \cC, \cD \subseteq \F_q$. The question of solvability of such and more general equations has recently been considered by Hart and Iosevich, who, in particular, prove that if for some absolute constant C > 0, then above equation has a solution for any λ ∈ q*. Here we show that using bounds of multiplicative character sums allows us to extend the class of sets which satisfy this property.

scholarly journals Character Sums, Primitive Elements, and Powers in Finite Fields

2001 ◽  
Vol 91 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Arne Winterhof
Keyword(s):  
Finite Fields ◽  
Character Sums ◽  
Primitive Elements
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