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2004 ◽  
Vol 47 (3) ◽  
pp. 553-556 ◽  
Author(s):  
Yann Bugeaud ◽  
Maurice Mignotte

AbstractWe study families of integer polynomials having roots very close to each other.AMS 2000 Mathematics subject classification: Primary 11C08


2004 ◽  
Vol 47 (2) ◽  
pp. 473-494 ◽  
Author(s):  
Fernando Rodriguez-Villegas ◽  
Ricardo Toledano ◽  
Jeffrey D. Vaaler

AbstractLet $L_{\bm{a}}(\bm{z})=a_1z_1+a_2z_2+\cdots+a_Nz_N$ be a linear form in $N$ complex variables $z_1,z_2,\dots,z_N$ with non-zero coefficients. We establish several estimates for the logarithmic Mahler measure of $L_{\bm{a}}$. In general, we show that the logarithmic Mahler measure of $L_{\bm{a}}(\bm{z})$ and the logarithm of the norm of $\bm{a}$ differ by a bounded amount that is independent of $N$. We prove a further estimate which is useful for making an approximate numerical evaluation of the logarithmic Mahler measure.AMS 2000 Mathematics subject classification: Primary 11C08; 11Y35; 26D15


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