ar X iv : 0 80 6 . 47 09 v 1 [ m at h . C A ] 2 8 Ju n 20 08 Retarded integral inequalities of Gronwall - Bihari type

ar X iv : 0 80 6 . 44 99 v 1 [ m at h . G N ] 2 7 Ju n 20 08 Aronszajn Compacta ∗

We consider a class of compacta X such that the maps from X onto metric compacta define an Aronszajn tree of closed subsets of X.

ar X iv : 0 80 6 . 27 19 v 1 [ m at h . G N ] 1 7 Ju n 20 08 A property of C p [ 0 , 1 ]

We prove that for every finite dimensional compact metric space X there is an open continuous linear surjection from Cp[0, 1] onto Cp(X). The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert’s

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 80 6 . 29 16 v 1 [ m at h . C A ] 1 8 Ju n 20 08 L 2 − interpolation with error and size of spectra

Given a compact set S and a uniformly discrete sequence Λ, we show that ”approximate interpolation” of delta–functions on Λ by a bounded sequence of L−functions with spectra in S implies an estimate on measure of S through the density of Λ.

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.