CORANSON-BEAUDU, Jean-Max

In this paper we show that Riemann's function (xi) , involving the Riemann's (zeta) function, is holomorphic and is expressed as a convergent infinite polynomial product in relation to their zeros and their conjugates. We take inspiration from the Weierstrass method to construct an infinite product model which is convergent and whose zeros are the ...

Halder, Samar Sahoo, Pulak
Published in
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)

AbstractWe study uniqueness problems in terms of shared values or shared sets for a large class of entire functions representable as Dirichlet series in some right half-plane. In this article, we obtain a result that extends a recent result due to Oswald and Steuding [Ann. Univ. Sci. Budapest., Sect. Comput. 48 (2018), 117–128 (2018)]. Our result i...

Garet, Olivier

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 ...

Merzlyakov, S. G.
Published in
Mathematical Notes

Abstract We prove an analogue of one of Cesàro’s results and use it to study the problem of interpolation by generalized exponential series, namely, by series whose terms themselves are Dirichlet series.

de la Bretèche, Régis Tenenbaum, Gérald

Let ρ be a complex number and let f be a multiplicative arithmetic function whose Dirichlet series takes the form ζ(s)^ρ G(s), where G is associated to a multiplicative function g. The classical Selberg-Delange method furnishes asymptotic estimates for the averages of f under assumptions of either analytic continuation for G, or absolute convergenc...

Chapoton, Frédéric Krattenthaler, Christian Zeng, Jiang

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.

Ech-chatbi, Charaf

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...

Elaissaoui, Lahoucine Guennoun, Zine El-Abidine

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...

Rotondo, Pablo

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 ...

CHOI, YUN SUNG KIM, UN YOUNG MAESTRE, MANUEL

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...