素数对于一类N-伯努利卷积谱对是完备的

中文摘要 AI 辅助

我们研究实线上一类自相似谱测度的完备数问题。对于谱对(μ,Λ)，若实数t满足tΛ也是μ的一个谱，则称t为完备数。本文考虑N-伯努利卷积μ_{N^r,𝒟}（其中𝒟={0,1,…,N-1}）及其谱Λ_{N^r,N^{r-1}𝒟}，主要结果证明除某些平凡情形外，每个素数都是完备数。

英文摘要

We study the complete number problem for a class of self-similar spectral measures on the real line. For a spectral pair $(μ,Λ)$, a real number $t$ is called complete if $tΛ$ is also a spectrum of $μ$. In this paper we consider the $N$-Bernoulli convolution $μ_{N^r,\mathcal D},\mathcal D=\{0,1,\ldots,N-1\},$ together with its spectrum $Λ_{N^r,N^{r-1}\mathcal D}.$ Our main result establishes that every prime number, apart from certain trivial cases, is complete.

发表机构

• Central China Normal University（华中师范大学）

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