Results 11 to 20 of about 151 (24)
Sequences of irreducible polynomials without prescribed coefficients over odd prime fields [PDF]
, 2013 In this paper we construct infinite sequences of monic irreducible polynomials with coefficients in odd prime fields by means of a transformation introduced by Cohen in 1992. We make no assumptions on the coefficients of the first polynomial $f_0$ of the
Ugolini, Simone
core +1 more source
Bernoulli-type Relations in Some Noncommutative Polynomial Ring [PDF]
, 2009 We find particular relations which we call "Bernoulli-type" in some noncommutative polynomial ring with a single nontrivial relation. More precisely, our ring is isomorphic to the universal enveloping algebra of a two-dimensional non-abelian Lie algebra.
Murata, Shunsuke
core +2 more sources
Explicit form of Cassels' $p$-adic embedding theorem for number fields [PDF]
, 2014 In this paper, we mainly give a general explicit form of Cassels' $p$-adic embedding theorem for number fields. We also give its refined form in the case of cyclotomic fields.
Dubickas, Arturas +2 more
core +3 more sources
Linear relations with conjugates of a Salem number [PDF]
, 2019 In this paper we consider linear relations with conjugates of a Salem number $\alpha$. We show that every such a relation arises from a linear relation between conjugates of the corresponding totally real algebraic integer $\alpha+1/\alpha$.
Dubickas, Artūras, Jankauskas, Jonas
core +3 more sources
, 2008 The aim of this note is to prove the Mahler measure identity $m(x+x^{-1}+y+y^{-1}+5) = 6 m(x+x^{-1}+y+y^{-1}+1)$ which was conjectured by Boyd.
Bertin M. J. +3 more
core +4 more sources
A generalization of a theorem of Boyd and Lawton
, 2012 The Mahler measure of a nonzero $n$-variable polynomial $P$ is the integral of $\log|P|$ on the unit $n$-torus. A result of Boyd and Lawton says that the Mahler measure of a multivariate polynomial is the limit of Mahler measures of univariate ...
Boyd +11 more
core +1 more source
On quotients of Riemann zeta values at odd and even integer arguments
, 2013 We show for even positive integers $n$ that the quotient of the Riemann zeta values $\zeta(n+1)$ and $\zeta(n)$ satisfies the equation $$\frac{\zeta(n+1)}{\zeta(n)} = (1-\frac{1}{n}) (1-\frac{1}{2^{n+1}-1}) \frac{\mathcal{L}^\star(\mathfrak{p}_n ...
Kellner, Bernd C.
core +1 more source
Higher Mahler measures and zeta functions
, 2009 We consider a generalization of the Mahler measure of a multivariable polynomial $P$ as the integral of $\log^k|P|$ in the unit torus, as opposed to the classical definition with the integral of $\log|P|$. A zeta Mahler measure, involving the integral of
Kurokawa, Nobushige +2 more
core +2 more sources
On the reducibility type of trinomials
, 2011 Say a trinomial $x^n+A x^m+B \in \Q[x]$ has reducibility type $(n_1,n_2,...,n_k)$ if there exists a factorization of the trinomial into irreducible polynomials in $\Q[x]$ of degrees $n_1$, $n_2$,...,$n_k$, ordered so that $n_1 \leq n_2 \leq ... \leq n_k$.
Bremner, Andrew, Ulas, Maciej
core +1 more source
Relative polynomial closure and monadically Krull monoids of integer-valued polynomials [PDF]
, 2015 Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N_0 ...
Frisch, Sophie
core