Discrete value-distribution of Artin LL-functions associated with cubic fields

Arising from the factorizations of Dedekind zeta-functions of non-Galois cubic fields, we obtain Artin $L$-functions of two-dimensional irreducible representations. In this paper, we study the distribution of values of such Artin $L$-functions as the cubic fields are varying. We prove that various mean values of the Artin $L$-functions are represented by integrals involving a density function which can be explicitly constructed. The result is applied to the study on the distribution of class numbers of cubic fields.Comment: 47 page

D-brane monodromies from a matrix-factorization perspective

The aim of this work is to analyze Kaehler moduli space monodromies of string compactifications. This is achieved by investigating the monodromy action upon D-brane probes, which we model in the Landau-Ginzburg phase in terms of matrix factorizations. The two-dimensional cubic torus and the quintic Calabi-Yau hypersurface serve as our two prime examples.Comment: 49 pages, 5 figures, harvmac; v2: minor changes and corrected typo

Matrix Factorizations and Homological Mirror Symmetry on the Torus

We consider matrix factorizations and homological mirror symmetry on the torus T^2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary moduli. We verify homological mirror symmetry by comparing three-point functions in the A-model and the B-model.Comment: 41 pages, 9 figures, v2: reference added, minor corrections and clarifications, version published in JHE

Matrix Factorizations, D-Branes and their Deformations

We review in elementary, non-technical terms the description of topological B-type of D-branes in terms of boundary Landau-Ginzburg theory, as well as some applications.Comment: 20p, 5 figs, Proceedings of Cargese school on string theory, 200