On the pure Jacobi sums
Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems
Comments on the height reducing property
A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus...
On the least common multiple of Lucas subsequences
We compare the growth of the least common multiple of the numbers and , where is a Lucas sequence and is some sequence of positive integers.
New criteria for canonical number systems
A self-similar tiling generated by the minimal Pisot number
Topological properties of two-dimensional number systems
In the two dimensional real vector space one can define analogs of the well-known -adic number systems. In these number systems a matrix plays the role of the base number . In the present paper we study the so-called fundamental domain of such number systems. This is the set of all elements of having zero integer part in their “-adic” representation. It was proved by Kátai and Környei, that is a compact set and certain translates of it form a tiling of the . We construct points, where...
Analytic continuation of multiple zeta-functions and their values at non-positive integers
Generalized radix representations and dynamical systems II
Connectedness of number theoretic tilings.
Basic properties of shift radix systems.
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