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

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

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

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

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

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

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

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

genetic algorithm | 11R06 | limit points | Mahler measure | MATHEMATICS

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2016, Volume 174, Issue 1, pp. 1 - 30

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

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

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

The Mahler measure provides a way to quantify the unstable and plays a key role in stabilization problems. This technical brief addresses the computation of...

Upper bound | Symmetric matrices | Uncertainty | Measurement uncertainty | robustness | Polynomials | Vectors | Eigenvalues and eigenfunctions | networked control system | Mahler measure | Linear matrix inequality (LMI) | uncertainty | LINEAR-SYSTEMS | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | ROBUST D-STABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Liapunov functions | Usage | Numerical analysis | Innovations | Eigenvalues | Simulation methods | Studies | Algorithms | Polytopes | Lyapunov functions | Stabilization | Upper bounds | Automatic control | Feasibility | Mathematical models

Upper bound | Symmetric matrices | Uncertainty | Measurement uncertainty | robustness | Polynomials | Vectors | Eigenvalues and eigenfunctions | networked control system | Mahler measure | Linear matrix inequality (LMI) | uncertainty | LINEAR-SYSTEMS | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | ROBUST D-STABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Liapunov functions | Usage | Numerical analysis | Innovations | Eigenvalues | Simulation methods | Studies | Algorithms | Polytopes | Lyapunov functions | Stabilization | Upper bounds | Automatic control | Feasibility | Mathematical models

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 10/2016, Volume 10, Issue 2, pp. 308 - 324

The purpose of this work is to give an asymptotic formula for the number of integer reducible polynomials with fixed degree 𝑑 ≥ 2 and Mahler measure bounded...

Integers | Algebra | Quadratic polynomials | Mathematical constants | Polynomials | Mathematical rings | Coefficients | Degrees of polynomials | Totally real algebraic integers | Reducible polynomials | Mahler measure | Polynomials with bounded zeros | MATHEMATICS | polynomials with bounded zeros | totally real algebraic integers | ALGEBRAIC-NUMBERS | MATHEMATICS, APPLIED | HEIGHT

Integers | Algebra | Quadratic polynomials | Mathematical constants | Polynomials | Mathematical rings | Coefficients | Degrees of polynomials | Totally real algebraic integers | Reducible polynomials | Mahler measure | Polynomials with bounded zeros | MATHEMATICS | polynomials with bounded zeros | totally real algebraic integers | ALGEBRAIC-NUMBERS | MATHEMATICS, APPLIED | HEIGHT

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

Higher Mahler measure | Mahler measure | MATHEMATICS

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 09/2015, Volume 197, pp. 49 - 61

For n≥1 let An≔{P:P(z)=∑j=1nzkj:0≤k1 Large sieve inequalities | [formula omitted] norm | Newman polynomials | Littlewood polynomials | Sums of monomials | Mahler measure | Fekete polynomials | Constrained coefficients | L 1 norm | INEQUALITIES | L-1 norm | REMEZ-TYPE | RESTRICTED COEFFICIENTS | SUBARCS | MATHEMATICS | BOUNDS | NORM | LARGE SIEVE | ZEROS

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

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

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

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

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

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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