Power series with non-negative non-increasing coefficients

Power Series with Integral Coefficients

Let f(z) be a function, meromorphic in \z\ < 1 , whose power series around the origin has integral coefficients. In [5], Salem shows that if there exists a nonzero polynomial p(z) such that p(z)f(z) is in H, or else if there exists a complex number a, such that l/(f(z)—a) is bounded, when |JS| is close to 1, then f(z) is rational. In [2], Chamfy extends Salem's results by showing that if there ...

Non-negative cd-coefficients of Gorensteinast posets

We give a convolution formula for cd-index coefficients. The convolution formula, together with the proof by Davis and Okun of the CharneyDavis Conjecture in dimension 3, imply that certain cd-coefficients are nonnegative for all Gorenstein* posets. Additional coefficients are shown to be non-negative by interpreting them in terms of the top homology of certain Cohen-Macaulay complexes. In part...

Multivariate Böttcher equation for polynomials with non-negative coefficients

Non-vanishing of Dirichlet series with periodic coefficients

Article history: Received 1 March 2014 Received in revised form 14 May 2014 Accepted 14 May 2014 Available online 3 July 2014 Communicated by Dinesh S. Thakur MSC: 11M06 11M20

On Nilpotent Power Series with Nilpotent Coefficients

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...