For a prime and positive integers with , we show that , the number of simultaneous solutions in to , , , satisfies
When we obtain a precise asymptotic count on . This leads to the new twisted exponential sum bound
for trinomials , and to results on the average size of such sums.
Pour un nombre premier et des entiers positifs avec , nous montrons que , le nombre de solutions simultanées dans de , , , satisfait à
Quand , nous obtenons un comptage asymptotique précis de . Cela conduit à une nouvelle borne explicite pour des sommes d’exponentielles tordues
pour des trinômes , et à des résultats sur la valeur moyenne de telles sommes.
Published online:
DOI: 10.5802/jtnb.533
Author's affiliations:
@article{JTNB_2006__18_1_59_0, author = {Todd Cochrane and Jeremy Coffelt and Christopher Pinner}, title = {A system of simultaneous congruences arising from trinomial exponential sums}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {59--72}, publisher = {Universit\'e Bordeaux 1}, volume = {18}, number = {1}, year = {2006}, doi = {10.5802/jtnb.533}, zbl = {05070447}, mrnumber = {2245875}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.533/} }
TY - JOUR TI - A system of simultaneous congruences arising from trinomial exponential sums JO - Journal de Théorie des Nombres de Bordeaux PY - 2006 DA - 2006/// SP - 59 EP - 72 VL - 18 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.533/ UR - https://zbmath.org/?q=an%3A05070447 UR - https://www.ams.org/mathscinet-getitem?mr=2245875 UR - https://doi.org/10.5802/jtnb.533 DO - 10.5802/jtnb.533 LA - en ID - JTNB_2006__18_1_59_0 ER -
Todd Cochrane; Jeremy Coffelt; Christopher Pinner. A system of simultaneous congruences arising from trinomial exponential sums. Journal de Théorie des Nombres de Bordeaux, Volume 18 (2006) no. 1, pp. 59-72. doi : 10.5802/jtnb.533. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.533/
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