Let be a rational function, with integer coefficients, satisfying rather general assumptions. We prove the existence of infinitely many integers , with exactly two prime divisors, such that the exponential sum is , where is a constant only depending on the geometrical data of . We also give Sato-Tate type results for some Salié sums modulo , with an integer as above.
Soit une fraction rationnelle à coefficients entiers, vérifiant des hypothèses assez générales. On prouve l’existence d’une infinité d’entiers , ayant exactement deux facteurs premiers, tels que la somme d’exponentielles soit en , où est une constante ne dépendant que de la géométrie de . On donne aussi des résultats de répartition du type Sato-Tate, pour certaines sommes de Salié, modulo , avec entier comme ci- dessus.
Mot clés : sommes d'exponentielles sur un corps fini, sommes de Kloosterman et de Salié, monodromie, loi de Sato-Tate, grand crible
Keywords: exponential sums over a finite field, Kloosterman and Salié sums, monodromy, Sato-Tate law, large sieve
Fouvry, Étienne 1; Michel, Philippe 2
@article{AIF_2002__52_1_47_0, author = {Fouvry, \'Etienne and Michel, Philippe}, title = {\`A la recherche de petites sommes d'exponentielles}, journal = {Annales de l'Institut Fourier}, pages = {47--80}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {1}, year = {2002}, doi = {10.5802/aif.1876}, zbl = {1014.11048}, mrnumber = {1881570}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1876/} }
TY - JOUR AU - Fouvry, Étienne AU - Michel, Philippe TI - À la recherche de petites sommes d'exponentielles JO - Annales de l'Institut Fourier PY - 2002 SP - 47 EP - 80 VL - 52 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1876/ DO - 10.5802/aif.1876 LA - fr ID - AIF_2002__52_1_47_0 ER -
%0 Journal Article %A Fouvry, Étienne %A Michel, Philippe %T À la recherche de petites sommes d'exponentielles %J Annales de l'Institut Fourier %D 2002 %P 47-80 %V 52 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1876/ %R 10.5802/aif.1876 %G fr %F AIF_2002__52_1_47_0
Fouvry, Étienne; Michel, Philippe. À la recherche de petites sommes d'exponentielles. Annales de l'Institut Fourier, Volume 52 (2002) no. 1, pp. 47-80. doi : 10.5802/aif.1876. https://aif.centre-mersenne.org/articles/10.5802/aif.1876/
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