Forms in many variables and differing degrees

DOI10.4171/JEMS/668zbMath1383.11039arXiv1403.5937OpenAlexW2963580186MaRDI QIDQ515325

D. R. Heath-Brown, Timothy D. Browning

Publication date: 13 March 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5937

zbMATH Keywords

exponential sumscomplete intersectionsrational pointscircle methodweak approximationforms in many variablesHasse principle

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Applications of the Hardy-Littlewood method (11P55) Counting solutions of Diophantine equations (11D45) Complete intersections (14M10) Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25)

Related Items

Solvable points on smooth projective varieties, Quadratic forms and systems of forms in many variables, Igusa's conjecture on exponential sums modulo \(p^m\) and the local-global principle, On the number of linear spaces on hypersurfaces with a prescribed discriminant, Geometric consistency of Manin's conjecture, Iteration of polynomials \(AX^d + C\) over finite fields, On forms in prime variables, Rational points on complete intersections over Fq(t)${\mathbb {F}}_q(t)$, The Manin–Peyre conjecture for smooth spherical Fano varieties of semisimple rank one, On the Hasse principle for complete intersections, ITERATION OF QUADRATIC POLYNOMIALS OVER FINITE FIELDS, FORMS OF DIFFERING DEGREES OVER NUMBER FIELDS, Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form, Applications of algebraic combinatorics to algebraic geometry, Systems of cubic forms in many variables, The density of rational lines on hypersurfaces: a bihomogeneous perspective, PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES, Failures of weak approximation in families, An exponential sum estimate for systems with linear polynomials, THE POWER‐SAVING MANIN–PEYRE CONJECTURE FOR A SENARY CUBIC

Cites Work

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• Varieties with too many rational points
• Rational points of bounded height on Fano varieties
• Heights and Tamagawa measures on Fano varieties
• Hypersurfaces of low degree
• The density of integer points on homogeneous varieties
• Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili
• Near-optimal mean value estimates for multidimensional Weyl sums
• A Variant of Weyl’s Inequality for Systems of Forms and Applications
• RATIONAL POINTS ON INTERSECTIONS OF CUBIC AND QUADRIC HYPERSURFACES
• Homogeneous forms of odd degree in a large number of variables
• Cubic forms in thirty-two variables
• Forms in many variables
• On some topics connected with Waring's problem.
• Vanishing Theorems, A Theorem of Severi, and the Equations Defining Projective Varieties
• Varieties of small codimension in projective space
• WEYL'S INEQUALITY AND SYSTEMS OF FORMS