One Relator Quotients of Graph Products

In this paper, we generalise Magnus' Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable polycyclic groups

A local global question in automorphic forms

In this paper, we consider the \SL(2) analogue of two well-known theorems about period integrals of automorphic forms on \GL(2): one due to Harder-Langlands-Rapoport, and the other due to Waldspurger.Comment: 28 page

Representations and KK-theory of Discrete Groups

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(B\Gamma)$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $\Gamma$.Comment: 4 page

Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

Point counting on reductions of CM elliptic curves

We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM $\mathbf{Q}$-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.Comment: Minor corrections. To appear in Journal of Number Theor

Quantitative Chevalley-Weil theorem for curves

The classical Chevalley-Weil theorem asserts that for an \'etale covering of projective varieties over a number field K, the discriminant of the field of definition of the fiber over a K-rational point is uniformly bounded. We obtain a fully explicit version of this theorem in dimension 1.Comment: version 4: minor inaccuracies in Lemma 3.4 and Proposition 5.2 correcte

Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction

We study electron molecules in realistic vertically coupled quantum dots in a strong magnetic field. Computing the energy spectrum, pair correlation functions, and dynamical form factor as a function of inter-dot coupling via diagonalization of the many-body Hamiltonian, we identify structural transitions between different phases, some of which do not have a classical counterpart. The calculated Raman cross section shows how such phases can be experimentally singled out.Comment: 9 pages, 2 postscript figures, 1 colour postscript figure, Latex 2e, Europhysics Letters style and epsfig macros. Submitted to Europhysics Letter

Culture as a moderator of cognitive age and travel motivation/perceived risk relations among seniors

Purpose - This study contributes to a greater understanding of the senior market and cultural differences relating to ageing in Western and Asian cultures. It highlights cultural differences toward the concept of ageing in Asian and Western countries and draws on a useful age concept for investigating senior consumers, namely, that of subjective age. The study aimed to investigate the influence of subjective age dimensions on seniors’ behavior, and to assess the role of culture as a moderator of this influence. Design/methodology/approach - Data were collected in France and Mainland China from 300 French seniors and 264 Chinese seniors respectively. Two main dimensions of subjective age were measured (cognitive age and ideal age), along with travel motivations and travel perceived risk. Findings - The study provides valuable information regarding the Western and Asian senior markets. Subjective age dimensions prove to be related to seniors’ behaviors (perceived travel risks). The present study also demonstrates that culture has a moderating role on this relation.  This theoretical contribution will have to be confirmed by other studies in Asian and Western countries; it opens the door to new research on Chinese/Asian seniors involving these age variables. Originality/Value – The study gives academics and managers insights into the influence of subjective age on seniors’ behaviours in Western and Asian cultural contexts