整数系数多项式的格:$L_2(0,1)$的连续极小值

IF 0.7 4区数学 Q2 MATHEMATICS

Annales Polonici Mathematici Pub Date : 2020-01-01 DOI:10.4064/ap190413-20-10

W. Banaszczyk

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引用次数: 0

摘要

．让Z P n成为《additive subgroup 2》真正的希尔伯特空间L (0, 1) consisting of polynomials of秩序和整数n≤coeﬃcients。我们可以在(n + 1) -次欧几里得空间中解决P - n的问题;让λi Z P (n)(1≤i≤n + 1) be the corresponding successive函数。我们给的很精确的保守λi n P (Z) for一世(cid): 38) 23 n。

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On the lattice of polynomials with integer coefficients: successive minima in $L_2(0,1)$

. Let P Z n 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 Z n as a lattice in ( n + 1) -dimensional Euclidean space; let λ i ( P Z n ) ( 1 ≤ i ≤ n + 1 ) be the corresponding successive minima. We give rather precise estimates of λ i ( P Z n ) for i (cid:38) 23 n .

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来源期刊

Annales Polonici Mathematici 数学-数学

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： Annales Polonici Mathematici is a continuation of Annales de la Société Polonaise de Mathématique (vols. I–XXV) founded in 1921 by Stanisław Zaremba. The journal publishes papers in Mathematical Analysis and Geometry. Each volume appears in three issues.