Vinogradov's mean value theorem via efficient congruencing. II

DOI10.1215/00127094-2079905zbMath1312.11066arXiv1112.0358OpenAlexW1981452459MaRDI QIDQ1949159

Trevor D. Wooley

Publication date: 25 April 2013

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

Full work available at URL: https://arxiv.org/abs/1112.0358

zbMATH Keywords

Waring's problemDiophantine systemssum-product theoremWeyl's inequalityestimates on exponential sumsVinogradov's integralTarry's problem

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Waring's problem and variants (11P05) Applications of the Hardy-Littlewood method (11P55) Weyl sums (11L15)

Related Items (36)

Almost primes of the form \(\lfloor p^c \rfloor\) ⋮ On the Vinogradov mean value ⋮ SOLUTIONS TO DIAGONAL CONGRUENCES WITH VARIABLES RESTRICTED TO A BOX ⋮ Near-optimal mean value estimates for multidimensional Weyl sums ⋮ On the Waring–Goldbach problem for eighth and higher powers ⋮ The asymptotic formula in Waring's problem: higher order expansions ⋮ Concentration of points on curves in finite fields ⋮ Restricted weak-type endpoint estimates for \(k\)-spherical maximal functions ⋮ Multigrade efficient congruencing and Vinogradov's mean value theorem ⋮ The cubic case of Vinogradov's mean value theorem ⋮ Explicit bounds for the Riemann zeta function and a new zero-free region ⋮ Analytic number theory in the last decade ⋮ APPROXIMATING THE MAIN CONJECTURE IN VINOGRADOV'S MEAN VALUE THEOREM ⋮ Random Diophantine equations. I ⋮ Points on curves in small boxes and applications ⋮ On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing ⋮ On sums of powers of almost equal primes ⋮ Rational lines on cubic hypersurfaces ⋮ Small fractional parts of polynomials ⋮ Small solutions of diagonal congruences ⋮ ON SOLUTIONS TO SOME POLYNOMIAL CONGRUENCES IN SMALL BOXES ⋮ Subgroups generated by rational functions in finite fields ⋮ Exponential sums involving the Möbius function ⋮ ON THE DISTRIBUTION OF POINTS ON THE GENERALIZED MARKOFF–HURWITZ AND DWORK HYPERSURFACES ⋮ Mixing for smooth time-changes of general nilflows ⋮ Simultaneous small fractional parts of polynomials ⋮ Averaging on thin sets of diagonal forms ⋮ WARING'S PROBLEM WITH PIATETSKI‐SHAPIRO NUMBERS ⋮ Bounds on short character sums and \(L\)-functions with characters to a powerful modulus ⋮ The asymptotic estimates and Hasse principle for multidimensional Waring's problem ⋮ On integer solutions of Parsell-Vinogradov systems ⋮ Polynomial values in affine subspaces of finite fields ⋮ Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values ⋮ Rational points on linear slices of diagonal hypersurfaces ⋮ MULTIPLE EXPONENTIAL AND CHARACTER SUMS WITH MONOMIALS ⋮ Sparse variance for \(k\)-free numbers in arithmetic progressions

Cites Work

• Vinogradov's mean value theorem via efficient congruencing
• Some remarks on Vinogradov's mean value theorem and Tarry's problem
• Trigonometric sums in number theory and analysis. Transl. from the Russian
• A note on simultaneous congruences
• On Weyl sums for smaller exponents
• The Asymptotic Formula in Waring’s Problem
• On the Bombieri–Korobov estimate for Weyl sums
• On Waring's problem for smaller exponents. II
• Weyl's Inequality, Hua's Inequality, and Waring's Problem
• On Vinogradov's mean value theorem
• Quasi-Diagonal Behaviour in Certain Mean Value Theorems of Additive Number Theory
• The asymptotic formula in Waring's problem
• A special case of Vinogradov's mean value theorem
• h-Fold Sums from a Set with Few Products
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Vinogradov's mean value theorem via efficient congruencing. II