@article{Zhang2023, 
author = {Jiafan Zhang},
title = {On the distribution of primitive roots and Lehmer numbers},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {11},
pages = {6913-6927},
keywords = {primitive roots, Lehmer numbers, Golomb's conjecture, Gauss sums, the generalized Kloosterman sums},
url = {https://www.sciopen.com/article/10.3934/era.2023350},
doi = {10.3934/era.2023350},
abstract = {In this paper, we study the number of the Lehmer primitive roots solutions of a multivariate linear equation and the number of    1  ≤  x  ≤  p  −  1 such that for    f  (  x  )  ∈                    F              p    [  x  ],    k polynomials    f  (  x  +      c    1    )  ,  f  (  x  +      c    2    )  ,  …  ,  f  (  x  +      c    k    ) are Lehmer primitive roots modulo prime    p, and obtain asymptotic formulae for these utilizing the properties of Gauss sums and the generalized Kloosterman sums.}
}