Rademacher sums, moonshine and gravity Export

@article{citeulike:5295919, abstract = {In 1939 Rademacher derived a conditionally convergent series expression for the elliptic modular invariant, and used this expression--the first Rademacher sum--to verify its modular invariance. By generalizing Rademacher's approach we construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for all groups commensurable with the modular group. We use these Rademacher sums to illuminate various aspects of the structure of the spaces of automorphic integrals, including the actions of Hecke operators. We obtain a new characterization of the discrete groups of monstrous moonshine in terms of Rademacher sums, and we develop connections between Rademacher sums and a family of monstrous Lie algebras recently introduced by Carnahan. Our constructions suggest conjectures relating monstrous moonshine to a distinguished family of chiral three dimensional quantum gravities, and relating monstrous Lie algebras and their Verma modules to the second quantization of this family of chiral three dimensional quantum gravities.}, archivePrefix = {arXiv}, author = {Duncan, John F. R. and Frenkel, Igor B.}, citeulike-article-id = {5295919}, citeulike-linkout-0 = {http://arxiv.org/abs/0907.4529}, citeulike-linkout-1 = {http://arxiv.org/pdf/0907.4529}, day = {25}, eprint = {0907.4529}, keywords = {math}, month = {Oct}, posted-at = {2009-10-27 12:44:00}, priority = {2}, title = {Rademacher sums, moonshine and gravity}, url = {http://arxiv.org/abs/0907.4529}, year = {2009} }

TY - JOUR ID - citeulike:5295919 L3 - citeulike-article-id:5295919 N2 - In 1939 Rademacher derived a conditionally convergent series expression for the elliptic modular invariant, and used this expression--the first Rademacher sum--to verify its modular invariance. By generalizing Rademacher's approach we construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for all groups commensurable with the modular group. We use these Rademacher sums to illuminate various aspects of the structure of the spaces of automorphic integrals, including the actions of Hecke operators. We obtain a new characterization of the discrete groups of monstrous moonshine in terms of Rademacher sums, and we develop connections between Rademacher sums and a family of monstrous Lie algebras recently introduced by Carnahan. Our constructions suggest conjectures relating monstrous moonshine to a distinguished family of chiral three dimensional quantum gravities, and relating monstrous Lie algebras and their Verma modules to the second quantization of this family of chiral three dimensional quantum gravities. TI - Rademacher sums, moonshine and gravity KW - math AU - Duncan, John AU - Frenkel, Igor PY - 2009/Oct/25/ UR - http://arxiv.org/abs/0907.4529 ER -