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Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2018, Volume 98, Issue 1, pp. 70 - 76
We give a lower bound of the Mahler measure on a set of polynomials that are 'almost' reciprocal. Here 'almost' reciprocal means that the outermost... 
Lehmer's conjecture | Mahler measure | polynomials | number theory | MATHEMATICS
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 07/2018, Volume 14, Issue 6, pp. 1605 - 1617
We study the Mahler measure of generators of a Galois extension with Galois group the full symmetric group. We prove that two classical constructions of... 
Lower bounds for the height | Mahler's measure | Lehmer's problem | MATHEMATICS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 04/2020, Volume 209, pp. 467 - 482
First, we give a formula for the limiting value of the higher Mahler measures for general polynomials of one variable, which refines Biswas and Monico's... 
Mahler measures | Zeta Mahler measures | Higher Mahler measures | Analytic continuation | MATHEMATICS
Journal Article
Constructive Approximation, ISSN 0176-4276, 6/2016, Volume 43, Issue 3, pp. 357 - 369
Littlewood polynomials are polynomials with each of their coefficients in $$\{-1,1\}$$ { - 1 , 1 } . A sequence of Littlewood polynomials that satisfies a... 
11C08 | 05D99 | 33E99 | Numerical Analysis | Analysis | Littlewood polynomials | Rudin–Shapiro polynomials | 41A10 | 11B75 | 11P99 | Mathematics | Mahler measure | SUBARCS | MATHEMATICS | BOUNDS | NORM | Rudin-Shapiro polynomials | FEKETE POLYNOMIALS | MOMENTS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2018, Volume 146, Issue 6, pp. 2359 - 2372
Given a k-variable Laurent polynomial F, any \ell \times k integer matrix A naturally defines an \ell -variable Laurent polynomial F_A. I prove that for fixed... 
Closure | Mahler measure | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | FEYNMAN-INTEGRALS | NUMBER | THEOREM | SEVERAL-VARIABLES | VALUES | closure | MONOMIALS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 04/2020, Volume 209, pp. 225 - 245
We prove an identity between two Mahler measures. Combining it with a result of Rogers and Zudilin, this leads to a formula relating the Mahler measure of a... 
Newton polygon | Mahler measure | Tempered polynomial | Elliptic curve | Elliptic regulator | Special values of L-functions | MATHEMATICS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2019, Volume 372, Issue 1, pp. 119 - 152
We develop a new method for relating Mahler measures of three-variable polynomials that define elliptic modular surfaces to L-values of modular forms. Using an... 
MATHEMATICS | REGULATOR | modular forms | elliptic surface | L-values | VALUES | Mahler measure | UNITS | Mathematics | Number Theory
Journal Article
Experimental Mathematics, ISSN 1058-6458, 04/2019, Volume 28, Issue 2, pp. 129 - 131
In this article, by the mean of genetic algorithms, we enlarge the list of known limit points of Mahler measures. 
genetic algorithm | 11R06 | limit points | Mahler measure | MATHEMATICS
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 09/2017, Volume 13, Issue 8, pp. 2195 - 2214
We prove an identity between Mahler measures of polynomials that was originally conjectured by Boyd. The combination of this identity with a result of Zudilin... 
elliptic curve | special values of L -functions | Mahler measure | elliptic regulator | MATHEMATICS | SPECIAL VALUES | special values of L-functions | UNITS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2009, Volume 129, Issue 7, pp. 1698 - 1708
Recently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metric naïve height on the multiplicative group of algebraic numbers.... 
Weil height | Lehmer's problem | Mahler measure | MATHEMATICS
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 12/2012, Volume 57, Issue 12, pp. 3208 - 3213
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 10/2016, Volume 10, Issue 2, pp. 308 - 324
Journal Article
Journal of Number Theory, ISSN 0022-314X, 10/2014, Volume 143, pp. 357 - 362
We consider the k-higher Mahler measure mk(P) of a Laurent polynomial P as the integral of logk|P| over the complex unit circle. In this paper we derive an... 
Higher Mahler measure | Mahler measure | MATHEMATICS
Journal Article
Journal Article
Experimental Mathematics, ISSN 1058-6458, 04/2016, Volume 25, Issue 2, pp. 107 - 115
We investigate the upper and lower bounds on the minimal Mahler measure of an irrational number lying in a particular real quadratic field. 
Primary 11R06 | Secondary 11C08 | Mahler measure | 11Y40 | MATHEMATICS | HEIGHT
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2016, Volume 283, Issue 3, pp. 1185 - 1193
We establish a general identity between the Mahler measures $$\mathrm {m}(Q_k(x,y))$$ m ( Q k ( x , y ) ) and $$\mathrm {m}(P_k(x,y))$$ m ( P k ( x , y ) ) of... 
Primary 11F67 | Elliptic integral | 11G16 | 14H52 | Mathematics | Mahler measure | Elliptic curve | Secondary 11F11 | 11F20 | 11G55 | 19F27 | L -value | 11R06 | Hyperelliptic curve | Mathematics, general | L-value | MATHEMATICS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2015, Volume 272, pp. 124 - 199
The Mahler measure of a polynomial is a measure of complexity formed by taking the modulus of the leading coefficient times the modulus of the product of its... 
Eigenvalue statistics | Matrix kernel | Mahler measure | Random polynomial | Pfaffian point process | Skew-orthogonal polynomials | UNIVERSALITY | ODD SIZE | ENSEMBLES | MATHEMATICS | EIGENVALUES | RANDOM MATRIX | ZEROS
Journal Article
CONSTRUCTIVE APPROXIMATION, ISSN 0176-4276, 08/2016, Volume 44, Issue 1, pp. 87 - 101
We prove Nikol'skii type inequalities that, for polynomials on the n-dimensional torus , relate the -norm with the -norm (with respect to the normalized... 
MATHEMATICS | INEQUALITIES | Khintchine-Kahane type inequality | HARDY-SPACES | Polynomials | Mahler measure | CIRCLE | Computer science
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 12/2016, Volume 181, Issue 4, pp. 907 - 935
The metric Mahler measure was first studied by Dubickas and Smyth in 2001 as a means of phrasing Lehmer’s conjecture in topological language. More recent work... 
Metric Mahler measure | 11A51 | 11J70 Secondary | Mathematics, general | Mathematics | Mahler measure | 11G50 | Height functions | Continued fractions | 11R09 Primary | MATHEMATICS | NUMBERS | Mathematics - Number Theory
Journal Article
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