A problem in additive number theory
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Publication:3801653
DOI10.1017/S0305004100064586zbMath0655.10041OpenAlexW2098833323MaRDI QIDQ3801653
Publication date: 1988
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0305004100064586
Hardy-Littlewood methodrepresentation of integersmean-value estimatemajor arcsmixed powerslarge integersHua's lemmacubic sumWeyl's inequality for quadratic exponential sum
Waring's problem and variants (11P05) Applications of the Hardy-Littlewood method (11P55) Representation problems (11D85)
Related Items (33)
A Ternary Problem in Additive Prime Number Theory ⋮ Sums of three cubes ⋮ On Waring-Goldbach problem of mixed powers ⋮ HUA‐TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS ⋮ On Waring's problem for four cubes ⋮ Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers ⋮ ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES ⋮ Sums of two unlike powers in arithmetic progressions ⋮ On the representation of integers as a sum of mixed powers ⋮ Sums of four cubes ⋮ Slim exceptional set for sums of mixed powers of primes ⋮ ON THE ASYMPTOTIC FORMULA IN WARING'S PROBLEM: ONE SQUARE AND THREE FIFTH POWERS ⋮ On smooth Weyl sums over biquadrates and Waring’s problem ⋮ A ternary additive problem ⋮ On Waring's problem for larger powers ⋮ On the Waring-Goldbach problem for two squares and four cubes ⋮ On Waring's problem: Beyond Freĭman's theorem ⋮ Subconvexity in the inhomogeneous cubic Vinogradov system ⋮ Vinogradov's mean value theorem via efficient congruencing ⋮ On the sum of four cubes ⋮ The representation of numbers as sums of unlike powers. II ⋮ Sums of cubes of square-free numbers. II ⋮ Additive representation in thin sequences, I: Waring's problem for cubes ⋮ The asymptotic formula in Waring's problem for one square and seventeen fifth powers ⋮ On Waring’s problem: Three cubes and a sixth power ⋮ Rational solutions of pairs of diagonal equations, one cubic and one quadratic ⋮ A Diophantine problem with unlike powers of primes ⋮ On Waring’s problem: Three cubes and a minicube ⋮ Representation by sums of unlike powers ⋮ On exceptional sets of biquadratic Waring-Goldbach problem ⋮ Even ascending powers ⋮ The representation of almost all numbers as sums of unlike powers ⋮ Rational points on linear slices of diagonal hypersurfaces
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