We explore some connections between moments of rescaled little q-Jacobi polynomials, q-analogues of values at negative integers for some Dirichlet series, and the q-Eulerian polynomials of wreath products of symmetric groups.
We present a proof of the Riemann's Zeta Hypothesis, based on asymp-totic expansions and operations on series. We use the symmetry property presented by Riemann's functional equation to extend the proof to the whole set of complex numbers C. The advantage of our method is that it only uses undergraduate maths which makes it accessible to a wider au...
We show that integrals involving the log-tangent function, with respect to any square-integrable function on , can be evaluated by the harmonic series. Consequently, several formulas and algebraic properties of the Riemann zeta function at odd positive integers are discussed. Furthermore, we show among other things, that the log-tangent integral w...
The aim of this note is to provide a Master Theorem for some discrete divide and conquer recurrences: $$X_{n}=a_n+\sum_{j=1}^m b_j X_{\lfloor p_j n \rfloor},$$ where the $p_i$'s belong to $(0,1)$. The main novelty of this work is there is no assumption of regularity or monotonicity for $(a_n)$. Then, this result can be applied to various sequences ...
Dynamical Analysis incorporates tools from dynamical systems, namely theTransfer Operator, into the framework of Analytic Combinatorics, permitting the analysis of numerous algorithms and objects naturally associated with an underlying dynamical system.This dissertation presents, in the integrated framework of Dynamical Analysis, the probabilistic ...
We study when the spaces of general Dirichlet series bounded on a half plane are Banach spaces, and show that some of those classes are isometrically isomorphic between themselves. In a precise way, let {lambda(n)} be a strictly increasing sequence of positive real numbers such that lim(n ->infinity) lambda(n) = infinity. We denote by H-infinity(la...
Published in Mathematical Notes
Power series whose coefficients are values of completely multiplicative functions from a general class determined by a small number of constraints are studied. The paper contains proofs of asymptotic estimates as such a power series tends to the roots of 1 along the radii of the unit circle, whence, in particular, it follows that these series canno...
Leukocyte infiltration plays critical roles in tissue inflammation for pathogen clearance and tumor eradication. This process is regulated by complex microenvironments in blood vessels, including inflamed endothelium, blood flow, and perivascular components. The role of perivascular components in leukocyte infiltration has not been systematically i...
Published in Mathematica Slovaca
In the present paper we introduce the upper and lower exponential density functions of subsets A ⊆ ℕ*. We identify completely the form of the upper density and find many properties for the lower one. We provide examples and list some open problems.
We study topics related to zeros of Dirichlet series and entire functions. A large part of the thesis is devoted to the location of zeros of Dirichlet series via density criteria. We establish the Nyman-Beruling criterion for a wide class of Dirichlet series and the Báez-Duarte criterion for Dirichlet L-functions in the semi-plane R(s)>1/p, for p ∈...
