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

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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Veröffentlicht in:The American mathematical monthly 2015-02, Vol.122 (2), p.138-142
1. Verfasser: de la Torre, Carlos A Catalá
Format: Artikel
Sprache:eng
Schlagworte:
Integrals
Number theory
Proof theory
Theorems
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Beschreibung
Zusammenfassung: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