Results 1 to 10 of about 151 (24)

Matrices induced by arithmetic functions acting on certain Krein spaces

Special Matrices, 2017
In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
Cho Ilwoo
doaj   +1 more source

Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs

Special Matrices, 2015
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the
Cho Ilwoo, Jorgensen Palle E. T.
doaj   +1 more source

Krein-space operators determined by free product algebras induced by primes and graphs

Special Matrices, 2017
In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
doaj   +1 more source

Squarefree values of polynomial discriminants II

Forum of Mathematics, Pi
We determine the density of integral binary forms of given degree that have squarefree discriminant, proving for the first time that the lower density is positive. Furthermore, we determine the density of integral binary forms that cut out maximal orders
Manjul Bhargava, Arul Shankar, Xiaoheng Wang   +2 more
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Improvements on dimension growth results and effective Hilbert’s irreducibility theorem

Forum of Mathematics, Sigma
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field.
Raf Cluckers, Pierre Dèbes, Yotam I. Hendel, Kien Huu Nguyen, Floris Vermeulen   +4 more
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Classification and irreducibility of a class of integer polynomials

Open Mathematics
We find all integer polynomials of degree dd that take the values ±1\pm 1 at exactly dd integer arguments, and determine the irreducibility of these polynomials by means of an elementary approach.
Chen Yizhi, Zhao Xiangui, Zhou Xuan
doaj   +1 more source

Reciprocal Monogenic Septinomials of Degree 2n3

Annales Mathematicae Silesianae
We prove a new irreducibility criterion for certain septinomials in ℤ[x], and we use this result to construct infinite families of reciprocal septinomials of degree 2n3 that are monogenic for all n ≥ 1.
Jones Lenny
doaj   +1 more source

Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations. [PDF]

Mon Hefte Math, 2023
Fadinger-Held V, Frisch S, Windisch D.
europepmc   +1 more source

A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator. [PDF]

Commun Algebra, 2020
Frisch S, Nakato S.
europepmc   +1 more source

Cycles of polynomial mappings in two variables over rings of integers in quadratic fields

Open Mathematics, 2004
Pezda T.
doaj   +1 more source