Cubic hypersurfaces and a version of the circle method for number fields

DOI10.1215/00127094-2738530zbMath1298.11098arXiv1207.2385OpenAlexW3101415518MaRDI QIDQ398990

Pankaj Vishe, Timothy D. Browning

Publication date: 18 August 2014

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.2385

zbMATH Keywords

hypersurfacecircle methodcubic formdelta methodnonsingularnumber fieldTen variables

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Applications of the Hardy-Littlewood method (11P55) Rational points (14G05) Other number fields (11R21) Diophantine equations in many variables (11D72) Cubic and quartic Diophantine equations (11D25)

Related Items (5)

On forms in prime variables ⋮ FORMS OF DIFFERING DEGREES OVER NUMBER FIELDS ⋮ Sieving rational points on varieties ⋮ On the Hasse principle for quartic hypersurfaces ⋮ Rational points on cubic hypersurfaces over \(\mathbb F_q(t)\)

Cites Work

• Bounds for automorphic \(L\)-functions
• Cubic polynomials over algebraic number fields
• Rational points on nonsingular cubic hypersurfaces
• La conjecture de Weil. I
• Cubic homogeneous polynomials over \(\mathfrak p\)-adic number fields
• Arithmetic on Some Singular Cubic Hypersurfaces
• A new form of the circle method, and its application to quadratic forms.
• Cubic Forms in Ten Variables
• A Poisson Summation Formula for Extensions of Number Fields
• Farey section in k ( i ) and k (ρ)
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