A note on points on algebraic sets

Year 2021, Volume: 50 Issue: 3, 821 - 824, 07.06.2021

Şermin Çam Çelik , Haydar Göral

https://doi.org/10.15672/hujms.743598

Abstract

In this short note, we count the points on algebraic sets which lie in a subset of a domain. It is proved that the set of points on algebraic sets coming from certain subsets of a domain has the full asymptotic. This generalizes the first theorem of [E. Alkan and E.S. Yörük, Statistics and characterization of matrices by determinant and trace, Ramanujan J., 2019] and also anwers some questions from the same article.

Keywords

algebraic sets, heights, asymptotics

References

• [1] E. Alkan and E.S. Yörük, Statistics and characterization of matrices by determinant and trace, Ramanujan J. 48, 131–149, 2019.
• [2] E. Bombieri and W. Gubler, Heights in Diophantine Geometry, Cambridge University Press; 1st edition, 2007.
• [3] D.H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. (2), 34, 461–479, 1933.