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Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
Lehmer's conjecture Hermitian matrices Eisenstein and Gaussian integers Number Theory
2012/6/29
We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least ...
The Prouhet-Tarry-Escott problem for Gaussian integers
The Prouhet-Tarry-Escott problem Gaussian integers
2010/11/11
Given natural numbers $n$ and $k$, with $n>k$, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of $\Z$, say $X=\{x_1,...,x_n\}$ and $Y=\{y_1,...,y_n\}$, such that \[x_1^i+...+x_n^i=y...