Rational points on linear slices of diagonal hypersurfaces

DOI10.1215/00277630-2891245zbMath1371.11139OpenAlexW1607531146MaRDI QIDQ5259314

Jörg Brüdern, Olivier Robert

Publication date: 26 June 2015

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

Full work available at URL: https://projecteuclid.org/euclid.nmj/1431347888

zbMATH Keywords

diagonal equationsrational pointscircle methodasymptotic formulalinear equationssimultaneous equationsadditive equations

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Rational points (14G05) Counting solutions of Diophantine equations (11D45) Weyl sums (11L15)

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Cites Work

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• Vinogradov's mean value theorem via efficient congruencing
• A new iterative method in Waring's problem
• On a certain nonary cubic form and related equations
• Vinogradov's mean value theorem via efficient congruencing. II
• On the representation of a number as the sum of two h-th powers
• The Asymptotic Formula in Waring’s Problem
• On simultaneous additive equations, III
• Forms in many variables
• Rational points on quartic hypersurfaces
• On Waring's problem for smaller exponents. II
• On Hua's estimates for exponential sums
• On nonary cubic forms.
• A problem in additive number theory
• On Another Sieve Method and the Numbers that are a Sum of Two h th Powers
• On simultaneous diagonal equations and inequalities
• On a New Technique and Its Applications to the Theory of Numbers
• A reduction technique in Waring's problem, I
• On nonary cubic forms: III.
• Some Diophantine equations with almost all solutions trivial
• Pairs of additive equations of small degree
• On another sieve method and the numbers that are a sum of two hth powers: II.
• MINOR ARC MOMENTS OF WEYL SUMS
• Répartition des points rationnels sur la cubique de Segre
• On the Hasse principle for cubic surfaces
• Simultaneous equations of additive type
• Cubic equations of additive type
• On nonary cubic forms: II.
• On Waring's problem for cubes.