关于 Cassels 与 Drungilas-Dubickas 的问题
数论
2016-06-09 v1
摘要
在关于多项式序列中光滑数的标准猜想假设下，我们肯定地回答了 Drungilas-Dubickas 的一个问题。这提供了反对“Dubickas 猜想”的证据，Ka\v{c}inskait\.e 和 Laurin\v{c}ikas 证明了该猜想蕴含了具有某些代数无理参数的 Hurwitz zeta 函数的普适性结果。在这些标准猜想下，我们还证明了一些结果，证实了 Worley 关于 Cassels 涉及代数数经整数平移后的乘法依赖性问题的观察。
关键词
引用
@article{arxiv.1606.02524,
title = {On questions of Cassels and Drungilas-Dubickas},
author = {Johan Andersson},
journal= {arXiv preprint arXiv:1606.02524},
year = {2016}
}
备注
10 pages, A version of this manuscript was circulated in a smaller group in July 2011. When looking at the manuscript this year I decided that it might have some interest for a wider circle. The current manuscript is very similar to the manuscript from 5 years ago, although I have rewritten the proofs to hold for algebraic numbers rather than algebraic integers