A New Proof for a Sharp van der Corput's Lemma

We give a simple proof of a sharper bound in a van der Corput's lemma found by K. Rogers in 2005. Continuity and a simple system of ODEs are used for proving the sharp bound. This lemma is of special interest in analytic number theory as well as the theory of oscillatory integrals, which appear...

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Bibliographic Details
Published inThe American mathematical monthly Vol. 122; no. 2; pp. 138 - 142
Main Author de la Torre, Carlos A Catalá
Format Journal Article
LanguageEnglish
Published Washington Mathematical Association of America 01.02.2015
Taylor & Francis Ltd
Subjects
Integrals
Number theory
Proof theory
Theorems
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Summary:We give a simple proof of a sharper bound in a van der Corput's lemma found by K. Rogers in 2005. Continuity and a simple system of ODEs are used for proving the sharp bound. This lemma is of special interest in analytic number theory as well as the theory of oscillatory integrals, which appear frequently throughout mathematics.
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.122.02.138