The Quarterly Journal of Mathematics - current issue

BI-ORDERINGS ON PURE BRAIDED THOMPSON'S GROUPS

Burillo, J., Gonzalez-Meneses, J. — 2008-02-21

In this paper it is proved that the pure braided Thompson's group BF admits a bi-order, analogously to the bi-order of the pure braid groups.

METAPLECTIC OPERATORS ON Cn

Feichtinger, H. G., Hazewinkel, M., Kaiblinger, N., Matusiak, E., Neuhauser, M. — 2008-02-21

The metaplectic representation describes a class of automorphisms of the Heisenberg group H = H(G), defined for a locally compact abelian group G. For G=R^d, H is the usual Heisenberg group. For the case when G is the finite cyclic group Z_n, only partial constructions are known. Here we present new results for this case and we obtain an explicit construction of the metaplectic operators on Cⁿ. We also include applications to Gabor frames.

THE DENSITY OF INTEGRAL POINTS ON COMPLETE INTERSECTIONS

Marmon, O. — 2008-02-21

In this paper, an upper bound for the number of integral points of bounded height on an affine complete intersection defined over Z is proven. The proof uses an extension to complete intersections of the method used for hypersurfaces by Heath-Brown (The density of rational points on non-singular hypersurfaces, Proc. Indian Acad. Sci. Math. Sci. 104 (1994) 13–29), the so called ‘q-analogue’ of van der Corput's AB process.

A NEW METHOD OF PRODUCING FUNCTIONAL RELATIONS AMONG MULTIPLE ZETA-FUNCTIONS

Matsumoto, K., Tsumura, H. — 2008-02-21

In this paper, we introduce a new method of producing functional relations among multiple zeta-functions. This method can be regarded as a kind of multiple analogue of Hardy's one of proving the functional equation for the Riemann zeta-function. Using this method, we give new functional relations for multiple zeta-functions. In particular, substituting positive integers into variables of them, we obtain known relation formulas for the multiple zeta-values. Furthermore, applying our method to a certain series involving hyperbolic sine functions, we can obtain certain multiple analogues of the known results given by Cauchy, Ramanujan, Berndt and so on.

ON THE STRUCTURE OF ASYMPTOTIC lp SPACES

Odell, E., Schlumprecht, Th., Zsak, A. — 2008-02-21

We prove that if X is a separable, reflexive space which is asymptotic l_p for some 1 ≤ p ≤ , then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition (FDD). This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic l_p FDD. More general results of this type are also obtained. As a consequence, we prove the existence of universal spaces for certain classes of separable, reflexive and asymptotic l_p spaces.

LABELLING THE CHARACTER TABLES OF SYMMETRIC AND ALTERNATING GROUPS

Wildon, M. — 2008-02-21

Let X be a character table of the symmetric group S_n. It is shown that unless n = 4 or n = 6, there is a unique way to assign partitions of n to the rows and columns of X so that for all and , X is equal to (), the value of the irreducible character of S_n labelled by on elements of cycle type . Analogous results are proved for alternating groups, and for the Brauer character tables of symmetric and alternating groups.