论文标题
广义差异集和自相关积分
Generalized difference sets and autocorrelation integrals
论文作者
论文摘要
在2010年，Cilleruelo，Ruzsa和Vinuesa在第一个$ N $自然数字中设置的广义Sidon的最大可能大小与在$ [0,1] $具有$ [0,1] $的非整合整体界限上的非阴性值的功能中建立了令人惊讶的联系。回答了Barnard和Steinerberger的最新问题，我们证明了关于所谓的广义差异集的最小大小的相应双重结果，该集合涵盖了第一个$ n $自然数，并且在类似问题中涉及$ \ Mathbb {r} $ autoCorrocorrelation intaforcorrelation interaforal interal intectal interal byne $ [0.0,1] $ [0.0,1] $ [0,0,1]。这些结果表明，Cilleruelo，Ruzsa和Vinuesa的对应关系代表了更普遍的现象，该现象将附加组合中的离散问题与连续世界中的问题有关。
In 2010, Cilleruelo, Ruzsa, and Vinuesa established a surprising connection between the maximum possible size of a generalized Sidon set in the first $N$ natural numbers and the optimal constant in an ``analogous'' problem concerning nonnegative-valued functions on $[0,1]$ with autoconvolution integral uniformly bounded above. Answering a recent question of Barnard and Steinerberger, we prove the corresponding dual result about the minimum size of a so-called generalized difference set that covers the first $N$ natural numbers and the optimal constant in an analogous problem concerning nonnegative-valued functions on $\mathbb{R}$ with autocorrelation integral bounded below on $[0,1]$. These results show that the correspondence of Cilleruelo, Ruzsa, and Vinuesa is representative of a more general phenomenon relating discrete problems in additive combinatorics to questions in the continuous world.
