Institute for Mathematical Physics on the Hardy–littlewood Majorant Problem on the Hardy-littlewood Majorant Problem
Institute for Mathematical Physics on the Hardy–littlewood Majorant Problem on the Hardy-littlewood Majorant Problem
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数学物理研究所 关于 Hardy-littlewood Majorant 问题 Hardy-littlewood Majorant 问题
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通讯作者：
I. Ruzsa
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作者：
B. Green;I. Ruzsa
设 Λ ⊆ {1,. .. , N }，令 {a n } n∈Λ 为具有 |a n | 的序列对于所有 n ≤ 1。很容易看出，对于每个偶数 p，n∈Λ a n e(nθ) p ≤ n∈Λ e(nθ) p。我们给出的例子表明，当 p 不是偶数时，该语句可能会显着失败。这对被称为哈代-利特尔伍德主要猜想的问题给出了否定的回答，从而排除了限制猜想和挂屋猜想家族的某种方法。
Let Λ ⊆ {1,. .. , N }, and let {a n } n∈Λ be a sequence with |a n | ≤ 1 for all n. It is easy to see that n∈Λ a n e(nθ) p ≤ n∈Λ e(nθ) p for every even integer p. We give an example which shows that this statement can fail rather dramatically when p is not an even integer. This answers in the negative a question known as the Hardy-Littlewood majorant conjecture, thereby ruling out a certain approach to the restriction and Kakeya families of conjectures.