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On the best approximation of non-integer constants by polynomials with integer coefficients

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Abstract

The exact decrease rate of the best approximations of non-integer numbers by polynomials with integer coefficients of growing degrees is found on a disk in the complex plane, a cube in ℝd, and a ball in ℝd. The sup-norm is used in the first two cases, and the norm in Lp, 1 ≤ p < ∞, is applied in the third one. Detailed comments are given (two remarks at the end of the paper).

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Authors and Affiliations

  1. Sumy State University, Sumy, Ukraine

    Roald M. Trigub

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  1. Roald M. Trigub
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Correspondence to Roald M. Trigub.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 20, No. 2, pp. 283–307, April–June, 2023

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Trigub, R.M. On the best approximation of non-integer constants by polynomials with integer coefficients. J Math Sci 274, 403–421 (2023). https://doi.org/10.1007/s10958-023-06609-5

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