ar X iv : 0 90 1 . 38 34 v 1 [ m at h . N T ] 2 4 Ja n 20 09 On the Inverse Problem Relative to Dynamics of the w Function

ar X iv : 0 90 6 . 32 38 v 1 [ m at h . N T ] 1 7 Ju n 20 09 GEOMETRIC AND p - ADIC MODULAR FORMS OF HALF - INTEGRAL WEIGHT by Nick

ar X iv : m at h / 05 01 14 5 v 1 [ m at h . D S ] 1 0 Ja n 20 05 WAVELET CONSTRUCTIONS IN NON - LINEAR DYNAMICS

We construct certain Hilbert spaces associated with a class of non-linear dynamical systems X. These are systems which arise from a generalized self-similarity, and an iterated substitution. We show that when a weight function W on X is given, then we may construct associated Hilbert spaces H(W) of L 2-martingales which have wavelet bases.

ar X iv : m at h - ph / 0 50 90 44 v 2 1 1 Ja n 20 06 RANDOM POLYNOMIALS , RANDOM MATRICES AND L - FUNCTIONS

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.

ar X iv : 0 90 1 . 37 00 v 1 [ he p - th ] 2 3 Ja n 20 09 The Path - Integral Approach to the N = 2 Linear Sigma Model

1 Abstract In QFT the effective potential is an important tool to study symmetry breaking phenomena. It is known that, in some theories, the canonical approach and the path-integral approach yield different effective potentials. In this paper we investigate this for the Euclidean N = 2 linear sigma model. Both the Green's functions and the effective potential will be computed in three different...

ar X iv : 0 90 1 . 18 06 v 1 [ m at h . A G ] 1 3 Ja n 20 09 GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES

We study the differential properties of generalized arc schemes and geometric versions of Kolchin’s Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.