Algebraic points on the projective line
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Schanuel’s formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of P1. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on P1 according as the height bound goes to ∞.
Abstract
Schanuel’s formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of P1. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on P1 according as the height bound goes to ∞.
참고문헌 (14)
- V. V. Batyrev, "Sur le nombre des points rationnels de hauteur born´e des vari´et´es alg´ebriques", Mathematische Annalen, 286통권 : 1, pp.27~43 (1990)
- V. V. Batyrev, "Rational points on some Fano cubic bundles", Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 323(1), pp.41~46 (1996)
- V. V. Batyrev, "Manin’s conjecture for toric varieties", Journal of Algebraic Geometry, 7(1), pp.15~53 (1998)
- J. Franke, "Rational points of bounded height on Fano varieties", Inventiones mathematicae, 95(2), pp.421~435 (1989)
- M. Hindry, "Diophantine Geometry. An Introduction, Graduate Texts in Mathematics, Vol. 201" (2000), Springer-Verlag
- S. Ih, "Height uniformity for algebraic points on curves", Compositio Mathematica, 134(1), pp.35~57 (2002)
- S. Lang, "Fundamentals of Diophantine Geometry" (1983), Springer-Verlag
- D. Masser, "Counting algebraic numbers with large height. II", Transactions of the American Mathematical Society, 359(1), pp.427~445 (2007)
- S. H. Schanuel, "Heights in number fields", Bulletin de la Société Mathématique de France, 107(4), pp.433~449 (1979)
- W. M. Schmidt, "Northcott’s theorem on heights. I. A general estimate", Monatsh Mathematical Physics, 115(1), pp.169~181 (1993)
- W. M. Schmidt, "Northcott’s theorem on heights. II. The quadratic case", Acta Arithmetica, 70(4), pp.343~375 (1995)
- J. H. Silverman, "The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics", pp.106~ (1986), Springer-Verlag
- J. H. Silverman, "Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics", pp.151~ (1994), Springer-Verlag
- P. Vojta, "Diophantine Approximations and Value Distribution Theory, Lecture Notes in Mathematics", pp.1239~ (1987), Springer-Verlag