Abstract
One approach to the Prouhet-Tarry-Escott problem is to construct products of the form
. This product has a zero of order N at 1, and the idea is to try to minimize the length (the l 1 norm) of p. We denote by E * N the minimum possible l 1 norm of any TV-term product of the above form. The l 1 norm is just the sum of the absolute values of the coefficients of the polynomial p when it is expanded, and an ideal solution of the Prouhet-Tarry-Escott problem arises when E * N = 2N (as in Theorem 1(c) of Chapter 11).
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Selected References
J. Bell, P. Borwein, and B. Richmond, Growth of the product \( \prod\nolimits_{{j = 1}}^n {\left( {1 - {x^{{{a_j}}}}} \right)} \), Acta Arith. 86 (1998), 115–130.
A.S. Belov and S.V. Konyagin, An estimate for the free term of a nonnegative trigonometric polynomial with integral coefficients, Mat. Zametki 59 (1996), 627–629.
P. Borwein and C. Ingalls, The Prouhet-Tarry-Escott problem revisited, Enseign. Math. (2) 40 (1994), 3–27.
P. Erdős and G. Szekeres, On the product \( \prod\nolimits_{{k = 1}}^n {\left( {1 - {z^{{{a_k}}}}} \right)} \), Acad. Serbe Sci. Publ. Inst. Math. 13 (1959), 29–34.
R. Maltby, Pure product polynomials and the Prouhet-Tarry-Escott problem, Math. Comp. 66 (1997), 1323–1340.
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© 2002 Springer-Verlag New York, Inc.
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Borwein, P. (2002). The Erdős—Szekeres Problem. In: Computational Excursions in Analysis and Number Theory. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21652-2_13
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DOI: https://doi.org/10.1007/978-0-387-21652-2_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3000-2
Online ISBN: 978-0-387-21652-2
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