We introduce and study elliptic zeta values, a two-parameter deformation of the values of Riemann’s zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share the SL(3,Z) modular properties of this function. Elliptic zeta values at even integers are related to Eisenstein series and thus to sums of odd powers of divisor...

Light-induced retinal degeneration is characterized by photoreceptor cell death. Many studies showed that photoreceptor demise is caspase-independent. In our laboratory we showed that leucocyte elastase inhibitor/LEI-derived DNase II (LEI/L-DNase II), a caspase-independent apoptotic pathway, is responsible for photoreceptor death. In this work, we investigated the activation of a pro-survival k...

Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring OP,X at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if OP,X is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré se...

The aim of this paper is to establish some properties solutions the Dirichlet–Neumann problem: $$(\partial _z\partial _{\overline{z}})^2 w=g$$ in unit disc $${{\mathbb {D}}}$$ , $$w=\gamma _0$$ and $$\partial _{\nu }\partial _{\overline{z}}w=\gamma $$ on $${\mathbb {T}}$$ (the circle), $$\frac{1}{2\pi i}\int _{{\mathbb {T}}}w_{\zeta {\overline{\zeta }}}(\zeta )\frac{d\zeta }{\zeta }=c$$ where _...

We compute the equivariant zeta function for bundles over infinite graphs and for infinite covers. In particular, we give a “transfer formula” for the zeta function of infinite graph covers. Also, when the infinite cover is given as a limit of finite covers, we give a formula for the limit of the zeta functions.

As analogue to special values at positive integers of the Riemann zeta function, we consider Carlitz zeta values ζC(n) at positive integers n. By constructing t-motives after Papanikolas, we prove that the only algebraic relations among these characteristic p zeta values are those coming from the Euler-Carlitz relations and the Frobenius p-th power relations.

In this article we compute a discrete mean value of the derivative of the Riemann zeta function. This mean value will be important for several applications concerning the size of ζ(ρ) where ζ(s) is the Riemann zeta function and ρ is a non-trivial zero of the Riemann zeta function.

We introduce a q-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple q-zeta values satisfy a q-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple q-zeta values can be viewed as special values of the multiple q-polylogarithm, which ad...

BACKGROUND Reducing the percentage of sperm anomalies in insemination samples remains a goal to be achieved in the intra-cytoplasmic sperm insemination (ICSI) procedure. The aim of this study was to evaluate the efficiency of density gradient centrifugation (DGC) and Zeta methods to recover sperm with intact chromatin, and to evaluate whether the combined DGC/Zeta procedure improved ICSI outcom...