The Critical Strips of the Sums 1 + 2z + ... + nz

We give a partition of the critical strip, associated with each partial sum 1 + 2z + ... + nz of the Riemann zeta function for Re z < −1, formed by infinitely many rectangles for which a formula allows us to count the number of its zeros inside each of them with an error, at most, of two zeros. A generalization of this formula is also given to a large class of almost-periodic functions with bounded spectrum.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

Privileged Regions in Critical Strips of Non-lattice Dirichlet Polynomials

This paper shows, by means of Kronecker’s theorem, the existence of infinitely many privileged regions called r -rectangles (rectangles with two semicircles of small radius r ) in the critical strip of each function Ln(z):= 1−∑nk=2kz , n≥2 , containing exactly [Tlogn2π]+1 zeros of Ln(z) , where T is the height of the r -rectangle and [⋅] represents the integer part.

The Gaia-ESO Survey: radial metallicity gradients and age-metallicity relation of stars in the Milky Way disk

We study the relationship between age, metallicity, and α-enhancement of FGK stars in the Galactic disk. The results are based upon the analysis of high-resolution UVES spectra from the Gaia-ESO large stellar survey. We explore the limitations of the observed dataset, i.e. the accuracy of stellar parameters and the selection effects that are caused by the photometric target preselection. We find that the colour and magnitude cuts in the survey suppress old metal-rich stars and young metal-poor stars. This suppression may be as high as 97% in some regions of the age-metallicity relationship. The dataset consists of 144 stars with a wide range of ages from 0.5 Gyr to 13.5 Gyr, Galactocentric distances from 6 kpcto 9.5 kpc, and vertical distances from the plane 0 < |Z| < 1.5 kpc. On this basis, we find that i) the observed age-metallicity relation is nearly flat in the range of ages between 0 Gyr and 8 Gyr; ii) at ages older than 9 Gyr, we see a decrease in [Fe/H] and a clear absence of metal-rich stars; this cannot be explained by the survey selection functions; iii) there is a significant scatter of [Fe/H] at any age; and iv) [Mg/Fe] increases with age, but the dispersion of [Mg/Fe] at ages >9 Gyr is not as small as advocated by some other studies. In agreement with earlier work, we find that radial abundance gradients change as a function of vertical distance from the plane. The [Mg/Fe] gradient steepens and becomes negative. In addition, we show that the inner disk is not only more α-rich compared to the outer disk, but also older, as traced independently by the ages and Mg abundances of stars.

On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.