International Mathematics Research Papers

Fox, Daniel J., F.

doi: 10.1155/IMRP.2005.461pmid: N/A

Abstract It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth functions on the cotangent bundle, fiberwise-polynomial of bounded degree, a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities), the star product is symmetric and specializes in the projectively flat case to the one constructed previously by C. Duval, P. Lecomte, and V. Ovsienko. These star products are built from a projectively invariant quantization map associating to a symmetric polyvector a formally selfadjoint operator on densities. A limiting form of this family of star products yields a commutative deformation of the symmetric tensor algebra of the manifold which is closely related to the limiting commutative multiplication of modular forms defined by P. Cohen, Y. Manin, and D. Zagier. A basic ingredient of the proof is the construction of projectively invariant multilinear differential operators on bundles of weighted symmetric k -vectors. The construction works except for a discrete set of excluded weights and generalizes the Rankin-Cohen brackets of modular forms. Erratum “Projectively invariant star products” dx.doi.org/10.1155/IMRP/2006/93234 This content is only available as a PDF. Copyright © 2005 Hindawi Publishing Corporation. All rights reserved.

Güloğlu, Ahmet Muhtar

doi: 10.1155/IMRN.2005.517pmid: N/A

We study the distribution of low lying zeroes assuming the generalized Riemann hypothesis of symmetric power L-functions associated to cusp forms of weight k for SL2 (ℤ) which are Hecke eigenforms. Following the theory of Katz and Sarnak and the approach of Iwaniec, Luo, and Sarnak (2000), we determine the symmetry type of the corresponding family of L-functions, thereby providing further evidence to the truth of density conjecture.

Ben Saïd, Salem; Ørsted, Bent

doi: 10.1155/IMRN.2005.551pmid: N/A

By taking an appropriate limit, we obtain the Bessel functions related to root systems as limits of Heckman-Opdam hypergeometric functions. A more general class of Bessel functions is also investigated, which we will call the Θ-Bessel functions. Explicit formulas for the Θ-Bessel functions are obtained when the multiplicity functions are even and positive integer-valued. This class encloses the Bessel functions on the tangent space at the origin of noncompact causal symmetric spaces, where an integral representation for these special functions is shown.