Theorem 2 is the main result in this note. Lemma 1 is key to our main result. It is different from the result in [2] because it does not restrict the number of terms in the partial sum to an even one. Also, our inequalities (2) should be compared with the corresponding result in [2] for k = 2. Lemma 1. Let sn(p) be the nth partial sum of the p-series ∑∞ i=1(1/i), and let k be any integer greate...

In this article, we generalize a result of Murty on the non-vanishing of complementary Bell numbers and irrationality of a p-adic series. This generalization leads to a sequence of polynomials. We partially answer the question of existence of an integral zero of those polynomials.

In the last nine years p-adic numbers have been successfully applied in various branches of theoretical and mathematical physics (for a review see [1-3]). One of the objects which we often encounter is a p-adic series. My interest in p-adic series is mainly motivated by the significant role they might play not only in pure but also in applied mathematics. It was initiated in 1987 [4] by an obse...

In a previous paper [3], the author gave an explicit description of the algebraic closure of the power series field over a field of characteristic p > 0, in terms of certain “generalized power series”. The purpose of the present paper is to extend this work to mixed characteristic. Specifically, we give an analogous description of the algebraic closure of the Witt ring W (K) of an algebraically...

Abstract We investigate some properties of complex structures on Lie algebras. In particular, we focus nilpotent that are characterised by suitable J -invariant ascending or descending central series, $\mathfrak {d}^{\,j}$ and {d}_j$ , respectively. introduce a new series {p}_j$ use it to prove characterisation structures. also examine whether stratified algebras preserve the strata. find there...

PURPOSE To compare changes in the corneal thickness profile before and 6 months after femtosecond laser in situ keratomileusis (LASIK) for hyperopia. METHODS In a prospective noncomparative case series study, 24 eyes of 20 hyperopic patients undergoing femtosecond LASIK were examined preoperatively and 6 months postoperatively. Corneal profile was measured using Pentacam HR device. Paired t t...

Mock modular forms are central objects in the recent discoveries of new instances of Moonshine. In this paper, we discuss the construction of mixed mock modular forms via integrals of theta series associated to indefinite quadratic forms. In particular, in this geometric setting, we realize Zwegers’ mock theta functions of type ( p, 1) as line integrals in hyperbolic p-space.