Inhomogeneous cubic congruences and rational points on del Pezzo surfaces

Stephan Baier; Tim D. Browning

doi:10.1515/crelle.2012.039

Inhomogeneous cubic congruences and rational points on del Pezzo surfaces

Stephan Baier^*, Tim D. Browning

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

14 Citations (Scopus)

Abstract

For given non-zero integers a, b, q we investigate the density of solutions (x, y) is an element of Z(2) to the binary cubic congruence ax(2) + by(3) 0 mod q, and use it to establish the Manin conjecture for a singular del Pezzo surface of degree 2 defined over (sic).

Translated title of the contribution	Inhomogeneous cubic congruences and rational points on del Pezzo surfaces
Original language	English
Pages (from-to)	69-151
Number of pages	83
Journal	Journal für die reine und angewandte Mathematik
Volume	680
DOIs	https://doi.org/10.1515/crelle.2012.039
Publication status	Published - Jul 2013

Keywords

MANINS CONJECTURE
FANO VARIETIES
BOUNDED HEIGHT
DENSITY
CURVES

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DIOPHANTINE GEOMETRY VIA ANALYTIC NUMBER THEORY
Browning, T. D. (Principal Investigator)
1/09/07 → 1/04/13
Project: Research

Cite this

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title = "Inhomogeneous cubic congruences and rational points on del Pezzo surfaces",

abstract = "For given non-zero integers a, b, q we investigate the density of solutions (x, y) is an element of Z(2) to the binary cubic congruence ax(2) + by(3) 0 mod q, and use it to establish the Manin conjecture for a singular del Pezzo surface of degree 2 defined over (sic).",

keywords = "MANINS CONJECTURE, FANO VARIETIES, BOUNDED HEIGHT, DENSITY, CURVES",

author = "Stephan Baier and Browning, {Tim D.}",

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language = "English",

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pages = "69--151",

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T1 - Inhomogeneous cubic congruences and rational points on del Pezzo surfaces

AU - Baier, Stephan

AU - Browning, Tim D.

PY - 2013/7

Y1 - 2013/7

N2 - For given non-zero integers a, b, q we investigate the density of solutions (x, y) is an element of Z(2) to the binary cubic congruence ax(2) + by(3) 0 mod q, and use it to establish the Manin conjecture for a singular del Pezzo surface of degree 2 defined over (sic).

AB - For given non-zero integers a, b, q we investigate the density of solutions (x, y) is an element of Z(2) to the binary cubic congruence ax(2) + by(3) 0 mod q, and use it to establish the Manin conjecture for a singular del Pezzo surface of degree 2 defined over (sic).

KW - MANINS CONJECTURE

KW - FANO VARIETIES

KW - BOUNDED HEIGHT

KW - DENSITY

KW - CURVES

U2 - 10.1515/crelle.2012.039

DO - 10.1515/crelle.2012.039

M3 - Article (Academic Journal)

SN - 1435-5345

VL - 680

SP - 69

EP - 151

JO - Journal für die reine und angewandte Mathematik

JF - Journal für die reine und angewandte Mathematik

ER -

Inhomogeneous cubic congruences and rational points on del Pezzo surfaces

Abstract

Keywords

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DIOPHANTINE GEOMETRY VIA ANALYTIC NUMBER THEORY

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