I know some basic bits about this construction as to how they effect permutations of Galois fields. But I want to get some detailed understanding of them. Any references?
2026-04-08 04:10:25.1775621425
From where can I study more about Dickson polynomials?
107 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in FIELD-THEORY
- Square classes of a real closed field
- Question about existence of Galois extension
- Proving addition is associative in $\mathbb{R}$
- Two minor questions about a transcendental number over $\Bbb Q$
- Is it possible for an infinite field that does not contain a subfield isomorphic to $\Bbb Q$?
- Proving that the fraction field of a $k[x,y]/(f)$ is isomorphic to $k(t)$
- Finding a generator of GF(16)*
- Operator notation for arbitrary fields
- Studying the $F[x]/\langle p(x)\rangle$ when $p(x)$ is any degree.
- Proof of normal basis theorem for finite fields
Related Questions in GALOIS-THEORY
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- A weird automorphism
- $S_3$ action on the splitting field of $\mathbb{Q}[x]/(x^3 - x - 1)$
- Question about existence of Galois extension
- Prove that K/L is a Galois extension
- discriminant and irreducibility of $x^p - (p+1)x - 1$
- galois group of irreducible monic cubic polynomial
- Proof of normal basis theorem for finite fields
- Regular inverse Galois problem for Q(t)
- When a certain subfield of $\mathbb{C}(x,y^2)$ is Galois
Related Questions in FINITE-FIELDS
- Covering vector space over finite field by subspaces
- Reciprocal divisibility of equally valued polynomials over a field
- Solving overdetermined linear systems in GF(2)
- Proof of normal basis theorem for finite fields
- Field $\mathbb{Q}(\alpha)$ with $\alpha=\sqrt[3]7+2i$
- Subfield of a finite field with prime characteristic
- Rank of a Polynomial function over Finite Fields
- Finite fields of order 8 and isomorphism
- Finding bases to GF($2^m$) over GF($2$)
- How to arrange $p-1$ non-zero elements into $A$ groups of $B$ where $p$ is a prime number
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Here are some good references. Some books that might help:
Dickson Polynomials by R. Lidl, G. Turnwald and G. Mullen
Finite Fields by R. Lidl and H. Niederreiter:
http://www.amazon.co.uk/Finite-Fields-Encyclopedia-Mathematics-Applications/dp/0521065674/ref=sr_1_fkmr0_1?ie=UTF8&qid=1435337437&sr=8-1-fkmr0&keywords=Finite+Fields+by+R.+Lidl+and+H.+Niederreiter
http://www.amazon.co.uk/Topics-Polynomials-Several-Variables-Applications/dp/9810206143/ref=sr_1_1?ie=UTF8&qid=1435337478&sr=8-1&keywords=Topics+in+Polynomials+of+One+and+Several+Variables+and+Their+Applications%3A+A+Legacy+of+P.L.Chebyshev
For some papers and notes on their relations to finite fields:
http://dept.math.lsa.umich.edu/~zieve/papers/manjul.pdf
http://ac.els-cdn.com/S1071579709000525/1-s2.0-S1071579709000525-main.pdf?_tid=12fa649e-1c24-11e5-8176-00000aacb361&acdnat=1435337876_e6802338fbe470e400c11d05eb8acc7b
http://people.math.carleton.ca/~wang/papers/genDickson.pdf
http://ac.els-cdn.com/0022314X88900066/1-s2.0-0022314X88900066-main.pdf?_tid=3a68ae6e-1c24-11e5-bc44-00000aacb35e&acdnat=1435337943_d76731b5b36282a2b6aba0afbabfe72c
http://personales.unican.es/gomezd/Articles/Winterhof/Waring_final.pdf
http://www.personal.psu.edu/jxs23/ReverseDP_2.pdf
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.7.8464&rep=rep1&type=pdf