We use the notion of covering sequence, introduced by C. Carlet and Y. Tarannikov, to give a simple characterization of bent functions. We extend it into a characterization of plateaued functions (that is bent and three-valued functions). After recalling why the class of plateaued functions provides good candidates to be used in cryptosystems, we study the known families of plateaued functions ...

We prove that the zero-set of a C∞ function belonging to a noetherian differential ring M can be written as a finite union of C∞ manifolds which are definable by functions from the same ring. These manifolds can be taken to be connected under the additional assumption that every zero-dimensional regular zero-set of functions in M consists of finitely many points. These results hold not only for...

Johnson [1] evaluated the sum d[n [C(d;r)[, where C(n;r) denotes Ramanujan’s trigonometric sum. This evaluation has been generalized to a wide class of arithmetical functions of two variables. In this paper, we generalize this evaluation to a wide class of arithmetical functions f several variables and deduce as special cases the previous evaluations.

The uncovering of new structure on the Cuntz semigroup a C*-algebra stable rank one leads to several applications: we answer affirmatively, for class rank-one C*-algebras, conjecture by Blackadar and Handelman dimension functions, global Glimm halving problem, problem realizing functions cone 2-quasitraces as ranks elements. We also gain insights into comparability properties positive elements ...