ar X iv : 0 90 6 . 55 92 v 2 [ nu cl - t h ] 1 6 Se p 20 09 Bulk Viscosity of Interacting Hadrons

ar X iv : 0 90 9 . 29 83 v 1 [ m at h . N T ] 1 6 Se p 20 09 COMBINATORIAL IDENTITIES INVOLVING THE MÖBIUS FUNCTION

In this paper we derive some identities and inequalities on the Möbius mu function. Our main tool is phi functions for intervals of positive integers and their unions.

ar X iv : 0 90 6 . 32 55 v 1 [ m at h . N T ] 1 7 Ju n 20 09 THE OVERCONVERGENT SHIMURA LIFTING by Nick Ramsey

— We construct a rigid-analytic map from the the author’s half-integral weight cuspidal eigencurve (see [10]) to its integral weight counterpart that interpolates the classical Shimura lifting.

ar X iv : 0 90 6 . 54 78 v 1 [ m at h - ph ] 3 0 Ju n 20 09 SPECTRAL AND SCATTERING THEORY OF SPACE - CUTOFF CHARGED P ( φ ) 2 MODELS

We consider in this paper space-cutoff charged P (ϕ) 2 models arising from the quantization of the non-linear charged Klein-Gordon equation: (∂t + iV (x)) 2 φ(t, x) + (−∆x + m 2)φ(t, x) + g(x)∂ z P (φ(t, x), φ(t, x)) = 0, where V (x) is an electrostatic potential, g(x) ≥ 0 a space-cutoff and P (λ, λ) a real bounded below polynomial. We discuss various ways to quantize this equation, starting fr...

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 : 0 90 6 . 33 84 v 1 [ m at h . A P ] 1 8 Ju n 20 09 ENERGY DISPERSED LARGE DATA WAVE MAPS IN 2 + 1 DIMENSIONS

In this article we consider large data Wave-Maps from R into a compact Riemannian manifold (M, g), and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive) concentration is absent. This is a companion to our concurrent article [21], which together with the present work establishes a full regularity theory for large data Wave-Maps.