Results 121 to 130 of about 99,592 (142)

Complementary Polynomials in Quantum Signal Processing. [PDF]

open access: yesCommun Math Phys
Berntson BK, Sünderhauf C.
europepmc   +1 more source

Algebraic-integer valued polynomials

Journal of Number Theory, 2022
Let \(R\) be a Dedekind domain of a global field \(K\). Let \(\mathrm{int}(n,R):=\{\alpha\in\overline{R}\mid [K(\alpha):K]=n\}\) and \(\mathrm{int}(\leq n,R):=\{\alpha\in\overline{R}\mid [K(\alpha):K]\leq n\}\). The main object of study of this paper is the ring \(\mathrm{Int}_K(E,\overline{R})\), that is the set of \(m\)-variate polynomials \(f\in K ...
openaire   +2 more sources

Integer-valued skew polynomials

Journal of Algebra and Its Applications, 2020
For a commutative integral domain [Formula: see text] with field of fractions [Formula: see text], the ring of integer-valued polynomials on [Formula: see text] is [Formula: see text]. In this paper, we extend this construction to skew polynomial rings. Given an automorphism [Formula: see text] of [Formula: see text], the skew polynomial ring [Formula:
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Split Quaternions and Integer-valued Polynomials

Communications in Algebra, 2014
The integer split quaternions form a noncommutative algebra over ℤ. We describe the prime and maximal spectrum of the integer split quaternions and investigate integer-valued polynomials over this ring. We prove that the set of such polynomials forms a ring, and proceed to study its prime and maximal ideals.
A. Cigliola, K. A. Loper, N. J. Werner
openaire   +1 more source

A Polynomial Taking Integer Values

Mathematics Magazine, 1996
In [2] Sury proves that for integers a, >j 2 1(ai aj) (i-j) is also an integer. (The result follows immediately from the theory of Lie groups; the number turns out to be the dimension of an irreducible representation of SU(n).) Sury gives an elementalry but indirect proof, based on the stronger result that H__ 2 i > j 2 (X1i-ai 1) (Xe-j 1) E Z[ X ...
openaire   +1 more source

Projective p-Orderings and Homogeneous Integer-Valued Polynomials

Integers, 2011
AbstractBhargava ...
Johnson, Keith, Patterson, Donald
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Integer-valued polynomials over block matrix algebras

Journal of Algebra and Its Applications, 2019
In this paper, we state a generalization of the ring of integer-valued polynomials over upper triangular matrix rings. The set of integer-valued polynomials over some block matrix rings is studied. In fact, we consider the set of integer-valued polynomials [Formula: see text] for each [Formula: see text], where [Formula: see text] is an integral ...
J. Sedighi Hafshejani   +2 more
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