منابع مشابه
Minimal Mahler Measures
We determine the minimal Mahler measure of a primitive, irreducible, noncyclotomic polynomial with integer coefficients and fixed degree D, for each even degree D ≤ 54. We also compute all primitive, irreducible, noncyclotomic polynomials with measure less than 1.3 and degree at most 44.
متن کاملIdentities between Mahler Measures
The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures (1) m(y + 2xy + y − x − 2x − x) = 5 7 m(y + 4xy + y − x + x) , which is one of many examples that arise from the comparison of Mahler measures and special values of L-functions [Bo], [De], [RV]. Let us recall that the logarithmic Mahler measure of a Laurent polynomial P ∈ C[x 1 , . ...
متن کاملThe values of Mahler measures
We investigate the set M∗ of numbers which occur as Mahler measures of integer polynomials and the subset M of Mahler measures of algebraic numbers (that is, of irreducible integer polynomials). We prove that every number α of degree d in M∗ is the Mahler measure of a separable integer polynomial of degree at most ∑ 1≤r≤d/2 ( d r ) with all its roots lying in the Galois closure F of Q(α), and e...
متن کاملHigher Mahler measures and zeta functions
We consider a generalization of the Mahler measure of a multivariable polynomial P as the integral of log |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 |P |s, is also considered. Specific examples are computed, yielding special values of zeta functions, Dirichlet L-functions, and polylogarithms.
متن کاملMahler measures and computations with regulators
In this work we apply the techniques that were developed in [M.N. Lalín, An algebraic integration for Mahler measure, Duke Math. J. 138 (2007), in press] in order to study several examples of multivariable polynomials whose Mahler measure is expressed in terms of special values of the Riemann zeta function or Dirichlet L-series. The examples may be understood in terms of evaluations of regulato...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2010
ISSN: 0208-6573
DOI: 10.7169/facm/1269437068