On Roots of Polynomials with Positive Coefficients
On rough and smooth neighbors.
We study the behavior of the arithmetic functions defined byF(n) = P+(n) / P-(n+1) and G(n) = P+(n+1) / P-(n) (n ≥ 1)where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.
On Rowland's sequence.
On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On -fibonomials.
On Saito-Kurokawa Descent for congruence subgroups.
On Schertz's class number formula related to elliptic units for some non-Galois extensions
On second 2-descent and non-congruent numbers
We use the so-called second 2-descent method to find several series of non-congruent numbers. We consider three different 2-isogenies of the congruent elliptic curves and their duals, and find a necessary condition to estimate the size of the images of the 2-Selmer groups in the Selmer groups of the isogeny.
On Selberg's Eigenvalue Conjecture.
On self-similar subgroups in the sense of IFS
In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterated function system (IFS). We then prove that some subgroups of -adic numbers are strong self-similar in the sense of IFS.
On semicontinuity of ramification invariants in dimension 2.
On semi-local binomial units in cubic number fields.
On semiregular digraphs of the congruence
We assign to each pair of positive integers and a digraph whose set of vertices is and for which there is a directed edge from to if . The digraph is semiregular if there exists a positive integer such that each vertex of the digraph has indegree or 0. Generalizing earlier results of the authors for the case in which , we characterize all semiregular digraphs when is arbitrary.
On semi-strong U-numbers
On Sequences satisfying .
On sequences of ±1's defined by binary patterns [Book]
On sequences of algebraic integers in pure extensions of prime degree
On sequences of numbers and polynomials defined by linear recurrence relations of order 2.
On sequences of positive integers
On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths
Let G be an additive finite abelian group. For every positive integer ℓ, let be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine for certain finite groups, including cyclic groups, the groups and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum subsequences...