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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 ...
Gaussian Behavior in Generalized Zeckendorf Decompositions
Fibonacci numbers Zeckendorf’s Theorem Lekkerkerker’s theorem generating functions partial fraction expansion central limit type theorems
2011/9/6
Abstract: A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $\{F_n\}_{n=1}^{\infty}$; Lekkerkerker proved that the avera...
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...
Gaussian concentration of the q-characters of the Hecke algebras of type A
Gaussian concentration q-characters of the Hecke algebras type A
2010/12/9
We show that with respect to the q-Plancherel measure on partitions of size n, the irreducible
characters of an Hecke algebra Hq(Sn) are concentrated around the normalized trace of Hq(Sn). More preci...