Incomplete character sums and a special class of permutations

Cohen, S. D.; Niederreiter, H.; Shparlinski, I. E.; Zieve, M.

Cohen, S. D. ; Niederreiter, H. ; Shparlinski, I. E. ; Zieve, M.

Journal de théorie des nombres de Bordeaux, Tome 13 (2001) no. 1, pp. 53-63.

Résumé
Abstract

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 $ℛ$ -orthomorphismes. Nous donnons quelques exemples de ces $ℛ$ -orthomorphismes.

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 $ℛ$ -orthomorphism. Examples of $ℛ$ -orthomorphisms are given.

MR Zbl

@article{JTNB_2001__13_1_53_0,
     author = {Cohen, S. D. and Niederreiter, H. and Shparlinski, I. E. and Zieve, M.},
     title = {Incomplete character sums and a special class of permutations},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {53--63},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {1},
     year = {2001},
     mrnumber = {1839900},
     zbl = {1065.11097},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_2001__13_1_53_0/}
}

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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, Tome 13 (2001) no. 1, pp. 53-63. http://archive.numdam.org/item/JTNB_2001__13_1_53_0/

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