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Zeta Functions and the Log-behavior of Combinatorial Sequences
log-convexity Riemann zeta function Bernoulli number Bell number Bessel zeta function Narayana number Hö lder's inequality
2014/6/3
In this paper, we use the Riemann zeta function ζ(x) and the Bessel zeta function ζμ(x) to study the log-behavior of combinatorial sequences. We prove that ζ(x) is log-convex for x>1. As a consequence...
Congruences of Multipartition Functions Modulo Powers of Primes
modular form partition multipartition Ramanujan-type congruence
2014/6/3
Let pr(n) denote the number of r-component multipartitions of n, and let Sγ λ be the space spanned by η(24z)γφ(24z), where η(z) is the Dedekind’s eta function and η(z) is a holomorphic modular form i...
Proof of a Positivity Conjecture on Schur Functions
symmetric function Schur function multiplier sequence totally positive sequence
2014/6/3
In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let (t)n denote the rising factorial, and let ΛR denote the a...
Partition Identities for Ramanujan's Third Order Mock Theta Functions
mock theta function Ramanujan's identities partition identity Fine's theorem involution
2014/6/3
We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions φ(-q) and ψ(-q). We also give an involution for Fine's partition identity on th...
We study the spectral functional A 7→ Tr f(D + A) for a suitable function f, a self-adjoint operator D having compact resolvent, and a certain class of bounded self-adjoint operators A.
Properties of harmonic meromorphic functions which are starlike of complex order with respect to conjugate points
harmonic meromorphic
2010/11/1
This paper defines and investigates a class of meromorphic univalent harmonic functions that are starlike of complex order with respect to conjugate points. The authors obtain convolution and convex c...
On certain subclass of harmonic univalent functions defined by a generalized Ruscheweyh derivatives operator
Harmonic univalent functions Ruscheweyh derivative
2010/9/20
In this paper, the class SH(α, β; n, λ) of univalent harmonic and sense-preserving mappings in the unit disk is introduced. The distortion inequalities and extreme points for functions in the class SH...
We characterize the connected components of the subset CN∗ of H∞ formed by the products bh, where b is Carleson-Newman Blaschke product and h ∈ H∞ is an inver-tible function.
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-calle...
The Spin-weighted Spheroidal Wave functions in the Case of s=1/2
Wave functions Mathematical Physics
2010/11/18
The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-p...
Length Functions for Semigroup Embeddings
Membership problem Word problem Embeddings of Semigroups
2010/12/6
Following the work done in [O] for groups, we describe, for a given semigroup S, which functions l : S → N can be realized up to equivalence as length functions g 7→ |g|H by embedding S into a finitel...
Multivalent meromorphic starlike functions with negative coefficients
Meromorphic Starlike Negative Coefficients
2010/9/13
Coefficient inequalities, distortion theorems and class preserving integral operators are obtained for p-valent meromorphic starlike functions of order α (0 ≤ α < p) with negative coefficients.
On fuzzy topological ring valued fuzzy continuous functions
fuzzy topological ring (FTR) fuzzy ideal
2010/9/13
The collection of all fuzzy continuous functions from a fts Y to a fuzzy topological ring (in short, FTR) Z, denoted by FC(Y,Z) induces a ring structure from that of Z. This paper explores the structu...
The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the
periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein seri...
Further Notes on a Family of Continuous, Non-differentiable Functions
continuous nowhere di erentiable fractal Hausdor dimension
2011/2/23
We examine a parametrized family of functions Fa, all of which are continuous and some of which are nowhere or almost nowhere di erentiable.