A new \(k\)th derivative estimate for exponential sums via Vinogradov's mean value

DOI10.1134/S0081543817010072zbMath1461.11110arXiv1601.04493OpenAlexW2963974820WikidataQ115526011 ScholiaQ115526011MaRDI QIDQ2362394

D. R. Heath-Brown

Publication date: 7 July 2017

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.04493

zbMATH Keywords

exponential sumsvan der Corput estimateVinogradov's mean value

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) (zeta (s)) and (L(s, chi)) (11M06) Trigonometric and exponential sums (general theory) (11L03)

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Cites Work

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• The cubic case of the main conjecture in Vinogradov's mean value theorem
• On van der Corput's \(k\)-th derivative test for exponential sums
• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Estimates of trigonometric sums by the third derivative
• Topics in multiplicative number theory
• An analog of van der Corput's A⁴-process for exponential sums
• VINOGRADOV'S INTEGRAL AND BOUNDS FOR THE RIEMANN ZETA FUNCTION
• Points Entiers Au Voisinage D'une Courbe, Sommes Trigonométriques Courtes ET Paires D'exposants

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