A generalization of a second irreducibility theorem of I. Schur
A generalization of a theorem by Cheo and Yien concerning digital sums.
A generalization of a theorem of Carlitz.
A generalization of a theorem of Erdös on asymptotic basis of order
Let be a system of disjoint subsets of . In this paper we examine the existence of an increasing sequence of natural numbers, , that is an asymptotic basis of all infinite elements of simultaneously, satisfying certain conditions on the rate of growth of the number of representations , for all sufficiently large and A theorem of P. Erdös is generalized.
A generalization of a theorem of Erdős-Rényi to m-fold sums and differences
Let m ≥ 2 be a positive integer. Given a set E(ω) ⊆ ℕ we define to be the number of ways to represent N ∈ ℤ as a combination of sums and differences of m distinct elements of E(ω). In this paper, we prove the existence of a “thick” set E(ω) and a positive constant K such that for all N ∈ ℤ. This is a generalization of a known theorem by Erdős and Rényi. We also apply our results to harmonic analysis, where we prove the existence of certain thin sets.
A generalization of a theorem of Euler for regular chains of complex quadratic irrationalities
A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
A generalization of a theorem of Minkowski
A generalization of a theorem of Schinzel
We give lower bounds for the Mahler measure of totally positive algebraic integers. These bounds depend on the degree and the discriminant. Our results improve earlier ones due to A. Schinzel. The proof uses an explicit auxiliary function in two variables.
A generalization of a third irreducibility theorem of I. Schur
A generalization of a unit index of Greither
A generalization of an Euler formula in partition theory
A generalization of an IMO problem.
A generalization of Atkinson's formula to L-functions
A generalization of Beatty's theorem.
A generalization of Bombieri's prime number theorem to algebraic number fields
A generalization of class formation by using hypercohomology.
A generalization of Cobham's theorem for regular sequences.
A generalization of Davenport's constant and its arithmetical applications
A generalization of Dirichlet's unit theorem
We generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a ℚ-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over ℚ retain their linear independence...