On the lattice of polynomials with integer coefficients: successive minima in L-2(0,1)

Banaszczyk Wojciech

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On the lattice of polynomials with integer coefficients: successive minima in L-2(0,1)

机译：晶格的多项式与整数在l2系数:连续最小值(0,1)

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摘要

Let P-n(z) be the additive subgroup of the real Hilbert space L-2(0, 1) consisting of polynomials of order <= n with integer coefficients. We may treat P-n(z) as a lattice in (n + 1)-dimensional Euclidean space; let lambda(i)(P-n(z)) (1 <= i <= n + 1) be the corresponding successive minima We give rather precise estimates of lambda(i)(P-n(z)) for i greater than or similar to 2/3n.

机译：让pn (z)的添加剂子群真实希尔伯特空间l2(0, 1)多项式组成< = n与整数系数。治疗pn (z)的晶格(n + 1)维耗散欧几里得空间;n + 1)是我们对应的连续的最小值给,而精确的估计λ(我)(pn (z))我大于或类似的2/3n。

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来源
《Annales Polonici Mathematici》 |2020年第2期|109-128|共20页
作者
Banaszczyk Wojciech;
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作者单位

Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland;

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正文语种英语
中图分类
关键词
crystal lattices; Integer; Hilbert spacePolynomial;

机译：晶体晶格;整数;希尔伯特spacePolynomial;

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On the lattice of polynomials with integer coefficients: successive minima in L-2(0,1)

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