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Let p, q, k and ℓ be positive integers. The (p , q , k , ℓ) -Fibonacci sequence (F k , ℓ , p , q) n ≥ 0 is the four-parameter sequence defined by the following recurrence F k , ℓ , p , q (n) = k F k , ℓ , p , q (n - p) + ℓ F k , ℓ , p , q (n - q) , with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, f (x) = x q - k x q - p - ℓ . [ABSTRACT FROM AUTHOR]

In 1972, Alniaçik proved that every strong Liouville number is mapped into the set of U m -numbers, for any non-constant rational function with coefficients belonging to an m-degree number field. In this paper, we generalize this result by providing a larger class of Liouville numbers (which, in particular, contains the strong Liouville numbers) with this same property (this set is sharp is a certain sense). [ABSTRACT FROM AUTHOR]