Results 1 to 10 of about 28 (21)
Splitting behavior of Sn-polynomials [PDF]
Research in Number Theory, 2015 We analyze the probability that, for a fixed finite set of primes S, a random, monic, degree n polynomial f(x)∈ℤ[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
J. Lagarias, Benjamin L. Weiss
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Functional equations for Mahler measures of genus-one curves [PDF]
, 2006 In this paper we will establish functional equations for Mahler measures of families of genus-one two-variable polynomials. These families were previously studied by Beauville, and their Mahler measures were considered by Boyd, Rodriguez-Villegas, Bertin,
Matilde Lal'in, Mathew Rogers
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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
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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.
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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.
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ON THE IRREDUCIBILITY OF SUM OF TWO RECIPROCAL POLYNOMIALS
, 2016 For a certain kind of reciprocal polynomials P (x), Q(x) ∈ Z[x], their sums are considered. We demonstrate that the Mahler measure of polynomials plays a role to prove the irreducibility of the sums over the field of rationals.
Minsang Bang, DoYong Kwon
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Products of quadratic polynomials with roots modulo any integer
, 2013 We classify products of three quadratic polynomials, each irreducible over Q, which are solvable modulo m for every integer m > 1 but have no roots over the rational numbers. Polynomials with this property are known as intersective polynomials.
Andrea M. Hyde, B. K. Spearman
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Squarefree values of polynomial discriminants II
Forum of Mathematics, PiWe 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 +2 more
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Classification and irreducibility of a class of integer polynomials
Open MathematicsWe 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
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Improvements on dimension growth results and effective Hilbert’s irreducibility theorem
Forum of Mathematics, SigmaWe 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 +4 more
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