Systems of bihomogeneous forms of small bidegree

Applications of the Hardy-Littlewood method (11P55) Counting solutions of Diophantine equations (11D45) Diophantine equations in many variables (11D72)

Cites Work

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Manin's conjecture for certain biprojective hypersurfaces
The Manin conjecture for \(x_0y_0+\dots+x_sy_s=0\)
Rational points of bounded height on Fano varieties
On the number of rational points of bounded height on algebraic varieties
Quadratic forms and systems of forms in many variables
Counting in hyperbolic spikes: The Diophantine analysis of multihomogeneous diagonal equations
Heights and Tamagawa measures on Fano varieties
Systems of cubic forms in many variables
The density of rational lines on hypersurfaces: a bihomogeneous perspective
Counting rational points on biprojective hypersurfaces of bidegree \((1,2)\)
The density of integer points on homogeneous varieties
Bihomogeneous forms in many variables
Systems of quadratic Diophantine inequalities
Counting rational points on biquadratic hypersurfaces
Systems of quadratic Diophantine inequalities and the value distribution of quadratic forms
Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
Points of bounded height on smooth hypersurfaces of toric varieties
A Variant of Weyl’s Inequality for Systems of Forms and Applications
On the Number of Rational Points of Bounded Height on Smooth Bilinear Hypersurfaces in Biprojective Space
Cubic forms in thirty-two variables
Forms in many variables
Rational points on some Fano cubic bundles
Arakelov Geometry and Diophantine Applications
WEYL'S INEQUALITY AND SYSTEMS OF FORMS
Points de hauteur bornée sur les hypersurfaces lisses de l'espace triprojectif

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