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arXiv · 2610.00386

New bounds for the integer Chebyshev constant of [0,1]

David Niedbala Giraudin
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Abstract

The integer Chebyshev constant of [0,1] has been bracketed by 0.4213 <= t_Z([0,1]) <= 0.422685 since the work of Pritsker (2005) and of Flammang (2014). We prove 0.4222286000 <= t_Z([0,1]) <= 0.4226846975, narrowing the interval from 1.39e-3 to 4.56e-4. Both bounds are established by explicit certificates. The upper bound is carried by an integer polynomial with 92 factors and explicit integer exponents; the lower bound by a discrete measure on 947 cells together with a library of 206 irreducible polynomials, through an inequality in which the terms paying for divisibility are made explicit. Two self-contained scripts, included as ancillary files, re-derive both bounds from the certificates alone.

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David Niedbala Giraudin. 2026-10-03. New bounds for the integer Chebyshev constant of [0,1]. https://arxiv.org/abs/2610.00386

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