Additive properties of subgroups of finite index in fields

作者：Berrizbeitia Pedro; Luca Florian^*

来源：Journal of Number Theory, 2011, 131(4): 605-617.

DOI：10.1016/j.jnt.2010.10.008

• Subgroups of finite index
• Fields
• Additive dimension
• Applications of sieve methods

In this paper, we confirm a conjecture of Bergelson and Shapiro concerning subgroups of finite index in multiplicative groups of fields which have maximal additive dimension. We also show that the natural extension of subgroups G(p) of prime index p inside Q* and additive dimension p + 1 to the case where p is replaced by a composite integer n leads to subgroups of bounded additive dimension on a set of positive integers n of asymptotic density 1.

• 出版日期2011-4