Resumen de Sequences of algebraic numbers and density modulo 1

Roman Urban

• We prove density modulo 1 of the sets of the form f¹m¸n» + rm : m; n 2 Ng and f¹m¸n» + rm+n¯ : m; n 2 Ng;

  where ¸; ¹ is a pair of rationally independent real algebraic numbers, satisfying some additional assumptions, » 6= 0, r; ¯ 2 R and rm is any sequence of real numbers.