scholarly journals An elementary inequality about the Mahler measure

2013 ◽  
Vol 6 (4) ◽  
pp. 393-397 ◽  
Author(s):  
Konstantin Stulov ◽  
Rongwei Yang
Keyword(s):  
Mahler Measure ◽  
Elementary Inequality

scholarly journals THE TOTAL DISTANCE FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS

2014 ◽  
Vol 90 (3) ◽  
pp. 391-403
Author(s):  
V. FLAMMANG
Keyword(s):  
Recursive Algorithm ◽  
Mahler Measure ◽  
Algebraic Integers ◽  
Numerical Examples ◽  
Auxiliary Functions ◽  
Total Distance ◽  
Totally Positive ◽  
Elementary Inequality

AbstractLet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}P(x)$ be a polynomial of degree $d$ with zeros $\alpha _1, \ldots, \alpha _d$. Stulov and Yang [‘An elementary inequality about the Mahler measure’, Involve6(4) (2013), 393–397] defined the total distance of$P$ as ${\rm td}(P)=\sum _{i=1}^{d} | | \alpha _i| -1|$. In this paper, using the method of explicit auxiliary functions, we study the spectrum of the total distance for totally positive algebraic integers and find its five smallest points. Moreover, for totally positive algebraic integers, we establish inequalities comparing the total distance with two standard measures and also the trace. We give numerical examples to show that our bounds are quite good. The polynomials involved in the auxiliary functions are found by a recursive algorithm.

scholarly journals Sums of monomials with large Mahler measure

2015 ◽  
Vol 197 ◽  
pp. 49-61 ◽  
Author(s):  
Stephen Choi ◽  
Tamás Erdélyi
Keyword(s):  
Mahler Measure

scholarly journals MAHLER MEASURE OF ‘ALMOST’ RECIPROCAL POLYNOMIALS

2018 ◽  
Vol 98 (1) ◽  
pp. 70-76
Author(s):  
J. C. SAUNDERS
Keyword(s):  
Lower Bound ◽  
Mahler Measure

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 coefficients of each polynomial mirror each other in proportion, while this pattern may break down for the innermost coefficients.

scholarly journals An elementary inequality

1979 ◽  
Vol 2 (3) ◽  
pp. 531-535 ◽  
Author(s):  
Seymour Haber
Keyword(s):  
Elementary Inequality

An elementary inequality is proved in this note.

scholarly journals Norms extremal with respect to the Mahler measure

2012 ◽  
Vol 132 (1) ◽  
pp. 275-300 ◽  
Author(s):  
Paul Fili ◽  
Zachary Miner
Keyword(s):  
Mahler Measure

scholarly journals Corrigendum: Bounding the Elliptic Mahler Measure II

2000 ◽  
Vol 62 (2) ◽  
pp. 640-640
Author(s):  
Graham Everest ◽  
Chris Pinner
Keyword(s):  
Mahler Measure
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