By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher’s and Almkvist-Granville’s Apéry-like formulae for odd zeta values. As a consequence, we get a new identity producing Apéry-like series for all ζ(2n+ 4m+ 3), n,m ≥ 0, convergent at the geometric rate with ratio 2−10.

A practical method to compute the Riemann zeta function is presented. The method can compute ζ(1/2 + it) at any T 1/4 points in [T, T + T 1/4] using an average time of T 1/4+o(1) per point. This is the same complexity as the Odlyzko-Schönhage algorithm over that interval. Although the method far from competes with the Odlyzko-Schönhage algorithm over intervals much longer than T 1/4, it still h...

The present study was initiated to understand the effect of PLGA concentration, PVA concentration, internal-external phase ratio, homogenization speed, and homogenization time on mean particle size, zeta potential, and percentage drug encapsulation using fractional factorial design. Using PLGA (50-50) as the carrier, hyaluronidase loaded PLGA nanoparticles were prepared using double emulsion so...

The simplest quartic field was introduced by M. Gras and studied by A. J. Lazarus. In this paper, we will evaluate the values of the Dedekind zeta functions at s = −1 of the simplest quartic fields. We first introduce Siegel’s formula for the values of the Dedekind zeta function of a totally real number field at negative odd integers, and will apply Siegel’s formula to the simplest quartic fiel...

We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to analyse. We prove that reduced zeta functions are multiplicative under certain conditions and investigate which reduced zeta functions have functional equations.

I survey some recent developments in the theory of zeta functions associated to infinite groups and rings, specifically zeta functions enumerating subgroups and subrings of finite index or finite-dimensional complex representations. 1. About these notes Over the last few decades, zeta functions have become important tools in various areas of asymptotic group and ring theory. With the first pape...

To probe Pol zeta functions in vivo via its error signature, here we report the properties of Saccharomyces cerevisiae Pol zeta in which phenyalanine was substituted for the conserved Leu-979 in the catalytic (Rev3) subunit. We show that purified L979F Pol zeta is 30% as active as wild-type Pol zeta when replicating undamaged DNA. L979F Pol zeta shares with wild-type Pol zeta the ability to per...

The occurrence of Hb H hydrops fetalis is reported for the first time. The mother has zeta-alpha thalassemia 1 (zeta zeta alpha alpha/----) and the father has non-deletion alpha thalassemia [zeta zeta alpha alpha/zeta zeta (alpha alpha)T]. The complete deletion of the zeta alpha cluster on one chromosome was confirmed by quantitation of alpha and zeta gene numbers, the normal alpha and zeta gen...

The alternating current electroosmotic flow of a non-Newtonian power-law fluid is studied in a circular microchannel. A numerical method is employed to solve the non-linear Poisson-Boltzmann and the momentum equations. The main parameters which affect the flow field are the flow behavior index, the dimensionless zeta potential and the dimensionless frequency. At very low dimensionless frequenci...

Protein kinase C-zeta (PKC-zeta) is a serine/threonine kinase downstream from phosphatidylinositol 3-kinase in insulin signaling pathways. However, specific substrates for PKC-zeta that participate in the biological actions of insulin have not been reported. In the present study, we identified insulin receptor substrate-1 (IRS-1) as a novel substrate for PKC-zeta. Under in vitro conditions, wil...