Exponential sums for O(2n+1,q) and their applications
Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 219-235
Voir la notice de l'article provenant de la source Cambridge University Press
For a nontrivial additive character \lambda and a multiplicative character \chi of the finite field with q elements (q a power of an odd prime), and for each positive integer r, the exponential sums \sum \lambda ((\tr w)^r) over w\in {SO}(2n+1,q) and \sum \chi (\det w)\lambda ((\tr w)^r) over {O}(2n+1,q) are considered. We show that both of them can be expressed as polynomials in q involving certain exponential sums. Also, from these expressions we derive the formulas for the number of elements w in {SO}(2n+1,q) and {O}(2n+1,q) with (\tr w)^r=\beta , for each \beta in the finite field with q elements.
Kim, Dae San. Exponential sums for O(2n+1,q) and their applications. Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 219-235. doi: 10.1017/S0017089501020079
@article{10_1017_S0017089501020079,
author = {Kim, Dae San},
title = {Exponential sums for {O(2n+1,q)} and their applications},
journal = {Glasgow mathematical journal},
pages = {219--235},
year = {2001},
volume = {43},
number = {2},
doi = {10.1017/S0017089501020079},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089501020079/}
}
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