论文标题
希尔伯特立方体的乘法性能
Multiplicative Properties of Hilbert Cubes
论文作者
论文摘要
我们在有限场中的希尔伯特立方体的基数上获得上限，避免了大型产品集和总和集的倒数。特别是，我们的结果取代了H.Hegyvári和P. P. Pach（2020）的最新估计，这些估计似乎是所有可接受参数的无效。我们的方法与H.Hegyvári和P. P. Pach的方法不同，并且基于A. A. A. Karatsuba（1991）和N. G. Moshchevitin（2007），基于任意集的双重特征和指数和指数和指数总和的界限。
We obtain upper bounds on the cardinality of Hilbert cubes in finite fields, which avoid large product sets and reciprocals of sum sets. In particular, our results replace recent estimates of N. Hegyvári and P. P. Pach (2020), which appear to be void for all admissible parameters. Our approach is different from that of N. Hegyvári and P. P. Pach and is based on some well-known bounds of double character and exponential sums over arbitrary sets, due to A. A. Karatsuba (1991) and N. G. Moshchevitin (2007), respectively.
