We consider a class of singular Riemannian manifolds, the deformed spheres S k , defined as the classical spheres with a one parameter family g[k] of singular Riemannian structures, that reduces for k = 1 to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian ∆SN k , we study the associated zeta functions ζ(s,∆SN k ). We introduce ...

We study the quantum effects in a brane-world model in which a constant curvature (in particular, a flat) brane universe is embedded in a higher-dimensional bulk AdS black hole, instead of the usual portion of the AdS5. By using zeta regularisation, we explicitly calculate the one-loop effective potential due to the bulk quantum fields and show that it leads to a non-vanishing cosmological cons...

INTRODUCTION 4 Introduction Zeta functions encoding geometric information such as zeta functions of algebraic varieties over finite fields or zeta functions of finite graphs will loosely be called geometric zeta functions in the sequel. Sometimes the geometric situation gives one tools at hand to prove analytical continuation, functional equation and an adapted form of the Riemann hypothesis. T...

Diacylglycerol kinase zeta is a member of the diacylglycerol kinase family of enzymes, which generate phosphatidic acid through diacylglycerol phosphorylation. In addition to the catalytic and cysteine-rich domains found in all diacylglycerol kinases, diacylglycerol kinase zeta has a MARCKS domain as well as a C-terminal region containing four ankyrin repeats and a PDZ-binding motif. Previous r...

The T-cell antigen receptor (TCR) is a complex of at least six different proteins (alpha, beta, gamma, delta, epsilon, and zeta) that is assembled in the endoplasmic reticulum (ER) and transported to the cell surface. Unlike mature T cells, most immature CD4+CD8+ thymocytes retain within the ER and degrade greater than 90% of some of the TCR components they synthesize, resulting in low surface ...

In [Iha86b], Ihara constructs a universal cocycle Gal ( Q/Q ) −→ Zp[[t0, t1, t∞]]/ ((t0 + 1)(t1 + 1)(t∞ + 1)− 1) arising from the action of Gal ( Q/Q ) on certain quotients of the Jacobians of the Fermat curves

In this paper, we show how to determine several properties of a finite graph G from its Ihara zeta function ZG(u). If G is connected and has minimal degree at least 2, we show how to calculate the number of vertices of G. To do so we use a result of Bass, and in the case that G is nonbipartite, we give an elementary proof of Bass’ result. We further show how to determine whether G is regular, a...

To a polynomial f over a p{adic eld K and a character of the group of units of the valuation ring of K one associates Igusa's local zeta function Z(s; f;), which is a meromorphic function on C. Several theorems and conjectures relate the poles of Z(s; f;) to the monodromy of f; the so{called holomorphy conjecture states roughly that if the order of does not divide the order of any eigenvalue of...

In this manuscript we show that function fields K|k with td(K|k) > dim(k)+1 can be recovered from their maximal pro-` abelian-by-central Galois theory, where dim(k) is the Kronecker dimension. This extends the main result of Pop [P5] beyond the case where k is an algebraic closure of a finite field. We also show how this implies the pro-` form of Ihara’s question / Oda-Matsumoto conjecture I/OM...

For K a field of characteristic zero, let M(K) denote the set of Drinfel’d associators defined over K [Dr]. The variety M is of great interest because of its connection to the deformations of universal enveloping algebras, fundamental group of the Teichmuller tower, and to Gal(Q/Q). There is a natural map M → A and for λ ∈ K, and Mλ is a torsor under GRT1 (= M0). If K << X,Y >> denotes the form...