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Arithmetical Applications of an Identity for the Vandermonde Determinant

D. S. Ramana
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Abstract

When $\{α_i\}_{1 \leq i \leq m}$ is a sequence of distinct non-zero elements of an integral domain $A$ and $γ$ is a common multiple of the $α_i$ in $A$ we obtain, by means of a simple identity for the Vandermonde determinant, a lower bound for $\sup_{1\leq i < j \leq m}ϕ(α_i - α_j)$ in terms of $ϕ(γ)$, where $ϕ$ is a function from the nonzero elements of $A$ to ${\bf R}_{+}$ satisfying certain natural conditions. We describe several applications of this bound.

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D. S. Ramana. 2007-03-10. Arithmetical Applications of an Identity for the Vandermonde Determinant. https://doi.org/10.4064/aa130-4-4

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