Oscillatory integrals with uniformity in parameters
Eren Mehmet Kıral1 ; Ian Petrow2 ; Matthew P. Young1
1 Department of Mathematics Texas A&M University College Station TX 77843-3368, U.S.A.
2 ETH Zürich - Departement Mathematik HG G 66.4 Rämistrasse 101 8092 Zürich, Switzerland
Journal de théorie des nombres de Bordeaux, Tome 31 (2019) no. 1, pp. 145-159.

Nous prouvons une formule asymptotique précise pour certains types d’intégrales oscillatoires que l’on peut traiter par la méthode de la phase stationnaire. Les estimations sont uniformes en termes de paramètres auxiliaires, ce qui est crucial pour les applications en théorie analytique des nombres.

We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is crucial for application in analytic number theory.

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Accepté le :
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DOI : 10.5802/jtnb.1072
Classification : 41A60, 42A38
Mots clés : Oscillatory integrals, Stationary phase
Eren Mehmet Kıral 1 ; Ian Petrow 2 ; Matthew P. Young 1

1 Department of Mathematics Texas A&M University College Station TX 77843-3368, U.S.A.
2 ETH Zürich - Departement Mathematik HG G 66.4 Rämistrasse 101 8092 Zürich, Switzerland
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Eren Mehmet Kıral; Ian Petrow; Matthew P. Young. Oscillatory integrals with uniformity in parameters. Journal de théorie des nombres de Bordeaux, Tome 31 (2019) no. 1, pp. 145-159. doi : 10.5802/jtnb.1072. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1072/

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