@article{booker_cohen_leong_trudgian_2022, 
  title={Primitive element pairs with a prescribed trace in the cubic extension of a finite field}, 
  DOI={10.48550/arxiv.2202.00829}, 
  abstractNote={We prove that for any prime power $q\notin\{3,4,5\}$, the cubic extension $\mathbb{F}_{q^3}$ of the finite field $\mathbb{F}_q$ contains a primitive element $ξ$ such that $ξ+ξ^{-1}$ is also primitive, and $\textrm{Tr}_{\mathbb{F}_{q^3}/\mathbb{F}_q}(ξ)=a$ for any prescribed $a\in\mathbb{F}_q$. This completes the proof of a conjecture of Gupta, Sharma, and Cohen concerning the analogous problem over an extension of arbitrary degree $n\ge3$.}, 
  publisher={arXiv}, 
  author={Booker, Andrew R. and Cohen, Stephen D. and Leong, Nicol and Trudgian, Tim}, 
  year={2022}, 
  month={Feb}
  }