A note on points on algebraic sets
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,
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- [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.
- Yayın Aralığı: 6
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi