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Lengths of factorizations of integer-valued polynomials on Krull domains with prime elements. [PDF]

Arch Math
Fadinger-Held V, Windisch D.
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Spectral quantum algorithm for passive scalar transport in shear flows. [PDF]

Sci Rep
Pfeffer P, Brearley P, Laizet S, Schumacher J.   +3 more
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Constructing families of 3-Selmer companions. [PDF]

Res Number Theory
Spencer H.
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Hypergeometric polynomials over finite fields

Hypergeometric polynomials over finite fields
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Multiplication of Polynomials over Finite Fields

SIAM Journal on Computing, 1990
Let GF(q) denote the Galois field on q elements, and let n denote a positive integer. Let \(\mu_ q(n)\) be the number of multiplications/divisions required to compute the coefficients of the product of a polynomial of degree \(n-1\) and a polynomial of degree n over GF(q) by means of linear algorithms.
Bshouty, Nader H., Kaminski, Michael
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Factoring Polynomials Over Finite Fields

Bell System Technical Journal, 1967
We present here an algorithm for factoring a given polynomial over GF(q) into powers of irreducible polynomials. The method reduces the factorization of a polynomial of degree m over GF(q) to the solution of about m(q − 1)/q linear equations in as many unknowns over GF(q).
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Polynomial Codes Over Certain Finite Fields

Journal of the Society for Industrial and Applied Mathematics, 1960
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Reed, I. S., Solomon, Gustave
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Polynomials over Finite Fields

2002
In all that follows F will denote a finite field with q elements. The model for such a field is ℤ/pℤ, where p is a prime number. This field has p elements. In general the number of elements in a finite field is a power of a prime, q = p f . Of course, p is the characteristic of F.
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Factoring Polynomials over a Finite Field

SIAM Journal on Applied Mathematics, 1978
The number of irreducible factors of a given monic polynomial $f( x )$ over $GF( q )$ is equal to the dimension of the space of characteristic sequences associated with $f( x )$. A basis for this space can be used to obtain the irreducible factors.
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