Abstract
The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in ℂ d . We study this problem on general sets but devote special attention to product sets such as cube and polydisk. We also establish a multivariate analog of the Hilbert–Fekete upper bound for the integer Chebyshev constant, which depends on the dimension of space. In the case of single-variable polynomials in the complex plane, our estimate coincides with the Hilbert–Fekete result.
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