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The Quarterly Journal of Mathematics 2001 52(1):89-105; doi:10.1093/qjmath/52.1.89
© 2001 by Oxford University Press
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Une estimation uniforme pour les intégrales simples à phase stationnaire

M. Redouaby1 and P. Sargos1

1 Institut Élie Cartan, Université Henri Poincaré (Nancy 1), 54506 Vandoeuvre-lès-Nancy, France, e-mail: redouaby{at}iecn.u-nancy.fr e-mail: sargos{at}iecn.u-nancy.fr

Nous apportons des précisions au lemme de la phase stationnaire concernant les intégrales oscillantes en dimension 1, prolongeant ainsi un résultat de Huxley (Glasgow Math. J. 36 (1994)). Nous appliquons ensuite notre résultat aux moyennes d'intégrales oscillantes lorsque la phase dépend régulièrement d'un paramètre, en prévision d'un article ultérieur sur les sommes d'exponentielles (en préparation).

Received 10 February 1998.


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