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.
@article{JTNB_2006__18_1_59_0, author = {Cochrane, Todd and Coffelt, Jeremy and Pinner, Christopher}, 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 = {http://archive.numdam.org/articles/10.5802/jtnb.533/} }
TY - JOUR AU - Cochrane, Todd AU - Coffelt, Jeremy AU - Pinner, Christopher TI - A system of simultaneous congruences arising from trinomial exponential sums JO - Journal de théorie des nombres de Bordeaux PY - 2006 SP - 59 EP - 72 VL - 18 IS - 1 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.533/ DO - 10.5802/jtnb.533 LA - en ID - JTNB_2006__18_1_59_0 ER -
%0 Journal Article %A Cochrane, Todd %A Coffelt, Jeremy %A Pinner, Christopher %T A system of simultaneous congruences arising from trinomial exponential sums %J Journal de théorie des nombres de Bordeaux %D 2006 %P 59-72 %V 18 %N 1 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.533/ %R 10.5802/jtnb.533 %G en %F JTNB_2006__18_1_59_0
Cochrane, Todd; Coffelt, Jeremy; Pinner, Christopher. 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. http://archive.numdam.org/articles/10.5802/jtnb.533/
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