Incomplete character sums and a special class of permutations
Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 1, p. 53-63

We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an -orthomorphism. Examples of -orthomorphisms are given.

Nous donnons une méthode pour majorer des sommes incomplètes des valeurs d’un caractère d’un groupe abélien fini, en des éléments générés par une récurrence d’. Cette méthode est particulièrement explicite lorsque la récurrence implique un type spécial de permutations, appelées -orthomorphismes. Nous donnons quelques exemples de ces -orthomorphismes.

@article{JTNB_2001__13_1_53_0,
     author = {Cohen, S. D. and Niederreiter, H. and Shparlinski, Igor E. and Zieve, M.},
     title = {Incomplete character sums and a special class of permutations},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {1},
     year = {2001},
     pages = {53-63},
     zbl = {1065.11097},
     mrnumber = {1839900},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2001__13_1_53_0}
}
Cohen, S. D.; Niederreiter, H.; Shparlinski, I. E.; Zieve, M. Incomplete character sums and a special class of permutations. Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 1, pp. 53-63. http://www.numdam.org/item/JTNB_2001__13_1_53_0/

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