Oscillatory integrals with uniformity in parameters
Eren Mehmet Kıral; Ian Petrow; Matthew P. Young
Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 1, p. 145-159

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.

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.

Received : 2018-03-03
Accepted : 2018-09-25
Published online : 2019-07-29
DOI : https://doi.org/10.5802/jtnb.1072
Classification:  41A60,  42A38
Keywords: Oscillatory integrals, Stationary phase
     author = {Eren Mehmet K\i ral and Ian Petrow and Matthew P. Young},
     title = {Oscillatory integrals with uniformity in parameters},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {1},
     year = {2019},
     pages = {145-159},
     doi = {10.5802/jtnb.1072},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2019__31_1_145_0}
Kıral, Eren Mehmet; Petrow, Ian; Young, Matthew P. Oscillatory integrals with uniformity in parameters. Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 1, pp. 145-159. doi : 10.5802/jtnb.1072. jtnb.centre-mersenne.org/item/JTNB_2019__31_1_145_0/

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