整个函数的指数类型下的'坑效应'及其维纳谱
The "pits effect" for entire functions of exponential type and the Wiener spectrum
AI总结：
本文研究了整个函数的零点等分布问题，提出一个简单的谱条件，适用于多种随机和伪随机序列，并揭示了梅比乌斯函数在二元 Chowla 猜想下的性质。
摘要：
给定一个序列ξ:Z_+→C，我们找到一个简单的谱条件，保证泰勒级数F_ξ(z)=∑_{n≥0}ξ(n)z^n/n!的零点在角域内等分布。该条件涵盖了已知的随机和伪随机序列实例，并提供了新的例子，包括Besicovitch几乎周期序列和乘法随机序列。此外，它还条件性地表明梅比乌斯函数μ在二元Chowla猜想下具有此性质。
英文摘要：
Given a sequence $ξ\colon \mathbb Z_+ \to \mathbb C$, we find a simple spectral condition which guarantees the angular equidistribution of the zeroes of the Taylor series \[ F_ξ(z) = \sum_{n\ge 0} ξ(n) \frac{z^n}{n!}\,. \] This condition yields practically all known instances of random and pseudo-random sequences $ξ$ with this property (due to Nassif, Littlewood, Chen-Littlewood, Levin, Eremenko-Ostrovskii, Kabluchko-Zaporozhets, Borichev-Nishry-Sodin), and provides several new ones. Among them are Besicovitch almost periodic sequences and multiplicative random sequences. It also conditionally yields that the Möbius function $μ$ has this property assuming "the binary Chowla conjecture".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
