Asymptotic estimates for rational linear spaces on hypersurfaces

DOI10.1090/S0002-9947-09-04821-1zbMath1181.11035OpenAlexW2064850466MaRDI QIDQ3629382

Scott T. Parsell

Publication date: 27 May 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-09-04821-1

zbMATH Keywords

exponential sumsHardy-Littlewood methodhomogeneous additive equationslinear spaces in hypersurfaces

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Applications of the Hardy-Littlewood method (11P55) Counting solutions of Diophantine equations (11D45) Diophantine equations in many variables (11D72) Higher degree equations; Fermat's equation (11D41) Hypersurfaces and algebraic geometry (14J70)

Related Items (3)

HUA‐TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS ⋮ Rational lines on cubic hypersurfaces ⋮ The asymptotic estimates and Hasse principle for multidimensional Waring's problem

Cites Work

• A new iterative method in Waring's problem
• Large improvements in Waring's problem
• A note on simultaneous congruences
• Multiple exponential sums over smooth numbers
• Homogeneous forms of odd degree in a large number of variables
• On Vinogradov's mean value theorem
• On exponential sums over smooth numbers.
• The density of rational lines on cubic hypersurfaces
• Pairs of additive equations of small degree
• A generalization of Vinogradov's mean value theorem
• Homogeneous additive equations
• A note on systems of homogeneous algebraic equations
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