Rational points of bounded height on Fano varieties

Frankē, Jens; Manin, Yuri I.; Tschinkel, Yuri

doi:10.1007/bf01393904

Cited by 274 publications

(132 citation statements)

References 7 publications

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“…This paper is part of a program, initiated in [19] and developed in [4], [30], [7], to relate asymptotics of points of bounded height to geometric and arithmetic invariants of X. For further results and motivating examples we refer to the book [31] and the papers [6], [38], [15] and [32].…”

Section: X)} (Where K X Is the Canonical Line Bundle Of X); • B(l) Ismentioning

confidence: 99%

Rational points on compactifications of semi-simple groups

Shalika

Takloo-Bighash

Tschinkel

2007

J. Amer. Math. Soc.

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Section: X)} (Where K X Is the Canonical Line Bundle Of X); • B(l) Ismentioning

confidence: 99%

Rational points on compactifications of semi-simple groups

Shalika

Takloo-Bighash

Tschinkel

2007

J. Amer. Math. Soc.

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“…P is the usual height on P 1 (Q) = P(Q)\G(Q) which is used in the study of height zeta functions for generalized flag varieties in [12]. Define the Eisenstein series E(s, g) by…”

Section: Eisenstein Seriesmentioning

confidence: 99%

Distribution of rational points of bounded height on equivariant compactifications of PGL 2 I

Takloo-Bighash

Tanimoto

2016

Res. number theory

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“…A conjecture of Manin (see [2]) predicts the asymptotic behavior of N U,H (B) as B tends to +∞, for some well-chosen Zariski open subset U of V, but the current technology is very far from allowing us to approach it for any surface V. A weaker version states that V has linear growth, by which we mean that there should exist an open subset U of V such that, for any fixed ε > 0,…”

Section: N Uh (B) = #{X ∈ U (Q) H (X) ≤ B}mentioning

confidence: 99%