Oscillatory integrals with uniformity in parameters
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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jtnb.1072
Classification : 41A60, 42A38
Mots clés : Oscillatory integrals, Stationary phase
Kıral, Eren Mehmet 1 ; Petrow, Ian 2 ; Young, Matthew P. 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
@article{JTNB_2019__31_1_145_0,
     author = {K{\i}ral, Eren Mehmet and Petrow, Ian and Young, Matthew P.},
     title = {Oscillatory integrals with uniformity in parameters},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {145--159},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {1},
     year = {2019},
     doi = {10.5802/jtnb.1072},
     mrnumber = {3994723},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.1072/}
}
TY  - JOUR
AU  - Kıral, Eren Mehmet
AU  - Petrow, Ian
AU  - Young, Matthew P.
TI  - Oscillatory integrals with uniformity in parameters
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2019
SP  - 145
EP  - 159
VL  - 31
IS  - 1
PB  - Société Arithmétique de Bordeaux
UR  - http://www.numdam.org/articles/10.5802/jtnb.1072/
DO  - 10.5802/jtnb.1072
LA  - en
ID  - JTNB_2019__31_1_145_0
ER  - 
%0 Journal Article
%A Kıral, Eren Mehmet
%A Petrow, Ian
%A Young, Matthew P.
%T Oscillatory integrals with uniformity in parameters
%J Journal de théorie des nombres de Bordeaux
%D 2019
%P 145-159
%V 31
%N 1
%I Société Arithmétique de Bordeaux
%U http://www.numdam.org/articles/10.5802/jtnb.1072/
%R 10.5802/jtnb.1072
%G en
%F 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, Tome 31 (2019) no. 1, pp. 145-159. doi : 10.5802/jtnb.1072. http://www.numdam.org/articles/10.5802/jtnb.1072/

[1] Blomer, Valentin; Khan, Rizwanur; Young, Matthew P. Distribution of Maass of holomorphic cusp forms, Duke Math. J., Volume 162 (2013) no. 14, pp. 2609-2644 | DOI | Zbl

[2] Conrey, John B.; Iwaniec, Henryk The cubic moment of central values of automorphic L-functions, Ann. Math., Volume 151 (2000) no. 3, pp. 1175-1216 | DOI | MR | Zbl

[3] Graham, Sidney W.; Kolesnik, Grigori van der Corput’s method of exponential sums, London Mathematical Society Lecture Note Series, 126, Cambridge University Press, 1991 | MR | Zbl

[4] Hörmander, Lars The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis, Classics in Mathematics, Springer, 2003 | Zbl

[5] Huxley, Martin N. Area, lattice points, and exponential sums, London Mathematical Society Monographs. New Series, 13, Oxford University Press, 1996 | MR | Zbl

[6] Iwaniec, Henryk; Kowalski, Emmanuel Analytic number theory, Colloquium Publications, 53, American Mathematical Society, 2004 | MR | Zbl

[7] Kıral, Eren Mehmet; Young, Matthew P. The fifth moment of modular L-functions (2017) (https://arxiv.org/abs/1701.07507)

[8] Petrow, Ian; Young, Matthew P. A generalized cubic moment and the Petersson formula for newforms, Math. Ann., Volume 373 (2019) no. 1-2, pp. 287-353 | DOI | MR | Zbl

[9] Stein, Elias M. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, 43, Princeton University Press, 1993 | MR | Zbl

[10] Zworski, Maciej Semiclassical analysis, Graduate Studies in Mathematics, 138, American Mathematical Society, 2012 | MR | Zbl

Cité par Sources :