First-generation E-commerce applications, such as corporate web sites or electronic catalogs have often been developed from a technological or marketing perspective. Technological features do not fit the customer’s requirements or marketing does not conceive E-commerce as part of their customer relationship program. Disappointing transaction figures or business cases for E-commerce are the most...

On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twisted by any homogeneous vector bundle is shown to be entire.

Let π be a partition. BG-rank(π) is defined as an alternating sum of parities of parts of π [1]. In [2], Berkovich and Garvan found theta series representations for the t-core generating functions P n≥0 at,j(n)q , where at,j(n) denotes the number of t-cores of n with BG-rank = j. In addition, they found positive eta-quotient representations for odd t-core generating functions with extreme value...

Cochran, Orr and Teichner introduced L–eta–invariants to detect highly non–trivial examples of non slice knots. Using a recent theorem by Lück and Schick we show that their metabelian L–eta–invariants can be viewed as the limit of finite dimensional unitary representations. We recall a ribbon obstruction theorem proved by the author using finite dimensional unitary eta–invariants. We show that ...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. If the fibers of G → B are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singer type formula. We also study traces on the corresponding algebras of pseudodifferentia...

Source-program modifications can make a partial evaluator yield dramatically better results. For example, eta-redexes can preserve static data flow by acting as an interface between values and contexts. This note presents a type-based explanation of what eta-expansion achieves, why it works, and how it can be automated. This leads to a unified view of various source-code improvements, including...

We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind–Mertens and prove the converse under suitable dimensionality restrictions.

We study interactions between the categories of D-modules on smooth and singular varieties. For a large class of singular varieties Y , we use an extension of the Grothendieck–Sato formula to show that DY -modules are equivalent to stratifications on Y , and as a consequence are unaffected by a class of homeomorphisms, the cuspidal quotients. In particular, when Y has a smooth bijective normali...

Inspired by Riemann’s work on certain quotients of the Dedekind Eta function, in this paper we investigate the value distribution of quotients of values of the Dedekind Eta function in the complex plane, using the form η(Ajz) η(Aj−1z) , where Aj−1 and Aj are matrices whose rows are the coordinates of consecutive visible lattice points in a dilation XΩ of a fixed region Ω in R, and z is a fixed ...