ar X iv : 0 90 6 . 32 49 v 1 [ m at h . N T ] 1 7 Ju n 20 09 THE HALF - INTEGRAL WEIGHT EIGENCURVE

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 . 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 . 48 35 v 1 [ m at h . O C ] 2 6 Ju n 20 09 The Complex Gradient Operator and the CR - Calculus

ar X iv : 0 90 6 . 18 57 v 1 [ m at h . C O ] 1 0 Ju n 20 09 On the circumference , connectivity and dominating cycles

Every 4-connected graph with minimum degree δ and connectivity κ either has a cycle of length at least 4δ − 2κ or has a dominating cycle.

ar X iv : 0 90 6 . 18 47 v 1 [ he p - la t ] 1 0 Ju n 20 09 Physical matrix elements for ∆ I = 3 / 2 channel K → ππ decays

are calculated on the RBC/UKQCD 32 3 × 64, L s = 16 lattices, using 2+1 dynamical flavors and domain wall fermions, with an inverse lattice spacing of a −1 = 2.42(4) GeV. Data is interpolated or extrapolated to energy conserving kinematics and a preliminary calculation of the experimental parameter |A 2 | is performed.