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...

Abstract. In this short paper we present a simple method for deriving a new and remarkable functional identity for Riemann’s Zeta Function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work ”Remarques sur un beau rapport entre les series des puissances tant directes que reciproques (E 352)” in Memoires de l’Academie des Sciences de Berlin 17, (1...

1. Unique Prime Factorization of Ideals: 21 September 2010 2 2. Minkowski Theory: 28 September 2010 5 October 2010 4 3. Cyclotomic Fields and Fermat: 6 13 October 2010 9 4. Multiplicative Minkowski and Dirichlet’s Unit Theorem: 19 26 October 2010 10 5. Factoring Rational Primes in Algebraic Number Fields: 26 October 2010 14 6. Application to Zeta Functions: 3 9 November 2010 18 7. Hilbert’s Ram...

denotes the average of f with respect to dPa ,N . Recently there has been considerable interest in the averages of products and ratios of the characteristic polynomials DN@m ,H#5P i51 N (m2xi(H)) of random matrices with respect to various ensembles. Such averages are used, in particular, in making predictions about the moments of the Riemann-zeta function @see Refs. 12–14 ~circular ensembles! a...

For smooth hyperbolic dynamical systems and smooth weights, we relate Ruelle transfer operators with dynamical Fredholm determinants and dynamical zeta functions: First, we establish bounds for the essential spectral radii of the transfer operator on new spaces of anisotropic distributions, improving our previous results [7]. Then we give a new proof of Kitaev’s [17] lower bound for the radius ...

We generalize the notion of a jet scheme (truncated arc space) to arbitrary fat points via adjunction, and show that this yields for each fat point, an endomorphism on each schemic Grothendieck ring as defined in [17]. We prove that some of the analogues for linear jets still hold true, like locally trivial fibration over the smooth locus. In this formalism, we can define several generating zet...

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 ...