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Incomplete character sums and a special class of permutations

S. D. Cohen, H. Niederreiter, I. E. Shparlinski, M. Zieve (2001)

Journal de théorie des nombres de Bordeaux

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.

Integers in number systems with positive and negative quadratic Pisot base

Z. Masáková, T. Vávra (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider numeration systems with base β and − β, for quadratic Pisot numbers β and focus on comparing the combinatorial structure of the sets Zβ and Z− β of numbers with integer expansion in base β, resp. − β. Our main result is the comparison of languages of infinite words uβ and u− β coding the ordering of distances between consecutive β- and (− β)-integers. It turns out that for a class of roots β of x2 − mx − m, the languages coincide, while for other quadratic Pisot numbers the language...

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