Let T be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over T , one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expre...

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponen...

Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the multiplicative anomaly issue is discussed. We look primordially into the zeta functions instead of the determinants themselves, as was done in previous work. That provid...

We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first-order transition, we observe a sharp rise in zeta/s near Tc. For constructions that exhibit a smooth cros...

The object of this paper is to identify the divided power series corresponding to the zeta measure associated to f f ,,[ r]. The first section introduces the zeta function for JF4[ T] and describes some of its interesting properties. In the second section, we describe results on interpolations and measures and state our main result (Theorem VII). The third section summarizes various results abo...

Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was o...

The infinite grid is the Cayley graph of Z × Z with the usual generators. In this paper, the Ihara zeta function for the infinite grid is computed using elliptic integrals and theta functions. The zeta function of the grid extends to an analytic, multivalued function which satisfies a functional equation. The set of singularities in its domain is finite. The grid zeta function is the first comp...

To characterize the function of the CD3 eta subunit of the T cell receptor (TCR), we have used cDNAs encoding CD3 zeta, CD3 eta, or both to reconstitute a variant of a cytochrome c-specific, I-Ek-restricted murine T cell hybridoma, termed MA5.8, which lacks CD3 zeta and CD3 eta proteins. We provide direct evidence that assembly and surface expression of TCRs can be mediated by either of these s...

DNA polymerase zeta (pol zeta), which is required for DNA damage-induced mutagenesis, functions in the error-prone replication of a wide range of DNA lesions. During this process, pol zeta extends from nucleotides incorporated opposite template lesions by other polymerases. Unlike classical polymerases, pol zeta efficiently extends from primer-terminal base pairs containing mismatches or lesion...

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...