On van der Corput's \(k\)-th derivative test for exponential sums

DOI10.1016/j.indag.2015.11.009zbMath1383.11096OpenAlexW2186725557MaRDI QIDQ266167

Olivier Robert

Publication date: 13 April 2016

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2015.11.009

zbMATH Keywords

exponential sumsDiophantine systemsvan der Corput's method

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Function spaces arising in harmonic analysis (42B35) Convergence and divergence of series and sequences (40A05) Trigonometric and exponential sums (general theory) (11L03)

Related Items (5)

A new \(k\)th derivative estimate for exponential sums via Vinogradov's mean value ⋮ Sums of certain fractional parts ⋮ Rational points on an intersection of diagonal forms ⋮ Stationary phase method, powers of functions, and applications to functional analysis ⋮ Unnamed Item

Cites Work

• On the fourth derivative test for exponential sums
• The cubic case of the main conjecture in Vinogradov's mean value theorem
• On the divisor and circle problems
• On the \(B\) transform of van der Corput
• Estimates of trigonometric sums by the third derivative
• Some exponent pairs by Vinogradov's method
• The multidimensional van der Corput transformation
• Decoupling, exponential sums and the Riemann zeta function
• A PAUCITY ESTIMATE RELATED TO NEWTON SUMS OF ODD DEGREE
• ERROR TERM IMPROVEMENTS FOR VAN DER CORPUT TRANSFORMS
• APPROXIMATING THE MAIN CONJECTURE IN VINOGRADOV'S MEAN VALUE THEOREM
• Some extremal functions in Fourier analysis
• Exponential Sums and the Riemann Zeta-Function II
• An analog of van der Corput's A⁴-process for exponential sums
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• Un Critère De La Dérivée Cinquième Pour Les Sommes D'Exponentielles
• An analogue of Van der Corput's A ⁵ ‐process for exponential sums
• Points Entiers Au Voisinage D'une Courbe, Sommes Trigonométriques Courtes ET Paires D'exposants
• Rational points on linear slices of diagonal hypersurfaces
• Sommes d'exponentielles avec dérivée troisième monotone
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