On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change

A coincidence between a hydrocarbon plasma absorption spectrum and the lambda 5450 DIB

The aim of this work is to link the broad lambda 5450 diffuse interstellar band (DIB) to a laboratory spectrum recorded through an expanding acetylene plasma. Cavity ring-down direct absorption spectra and astronomical observations of HD 183143 with the HERMES spectrograph on the Mercator Telescope in La Palma and the McKellar spectrograph on the DAO 1.2 m Telescope are compared. In the 543-547 nm region a broad band is measured with a band maximum at 545 nm and FWHM of 1.03(0.1) nm coinciding with a well-known diffuse interstellar band at lambda 5450 with FWHM of 0.953 nm. A coincidence is found between the laboratory and the two independent observational studies obtained at higher spectral resolution. This result is important, as a match between a laboratory spectrum and a - potentially lifetime broadened - DIB is found. A series of additional experiments has been performed in order to unambiguously identify the laboratory carrier of this band. This has not been possible. The laboratory results, however, restrict the carrier to a molecular transient, consisting of carbon and hydrogen.Comment: 6 pages, 3 figures, accepted for publication in A&

MATRIX SPECTROSCOPY OF PEROXYL RADICALS VIA A HYPERTHERMAL NOZZLE

Author Institution: Dept. Chemistry, University of Colorado Boulder; Center for Renewable Chemical Technologies \& Materials, NRELWe have developed a hyperthermal nozzle to produce organic radicals for study in a cryogenic matrix. This hot nozzle thermally decomposes organic precursors in a stream of Ar and produces roughly $10^{13}$ hydrocarbon radicals/pulse. This technique has enabled us to prepare alkylperoxyl radicals by co-deposition with oxygen. In the atmospheric ?processing? of organic aerosols, surface bound peroxyl radicals will be important reaction intermediates. We have successfully studied the CH3OO radical by combining $CH_{3}$ and $O_{2}$ in an Ar matrix at 20 K. Preliminary results for allylperoxyl $(CH_{2}CHCH_{2}OO)$ and propargylperoxyl $(HCCCH_{2}OO)$ radical will be presented

MATRIX SPECTROSCOPY OF THE PROPARGYL RADICAL AND PROPARGYL PEROXYL RADICAL

Author Institution: Dept. Chemistry, University of Colorado Boulder; Dept. Chemistry, Center for Renewable Chemical Technologies \& MaterialsUsing a hyperthermal nozzle that we have developed we have produced propargyl radical ($HC\equiv CCH_{2}$) from the pyrolysis of propargyl bromide and butyn nitrite. Matrix isolated IR spectra and linear dichroism spectra were recorded, and vibrational symmetries were assigned. Photoionization mass spectrometry also confirmed the formation of propargyl radical. This hot nozzle thermally decomposes organic precursors in a stream of Ar and produces roughly $10^{13}$ hydrocarbon radicals/pulse. Using time of flight mass spectrometry and matrix isolated IR spectroscopy we have also observed the bimolecular self reaction of propargyl to form benzene, $C_{3}H_{3} + C_{3}H_{3} \rightarrow C_{6}H_{6}$. IR spectra also show that the formation of $CH_{3}-C\equiv CH$ and $CH_{2}=C=CH_{2}$ occurs in the hyperthermal nozzle. Co-depositing the propagyl radical with molecular oxygen allows us to synthesize the propagyl peroxyl radical ($H-C\equiv C-CH_{2}OO$), which we have characterized in the infrared as well

THE ROLE OF A NOVEL DIRADICAL PATHWAY IN REACTIONS BETWEEN PEROXYL RADICALS AND NO

Author Institution: Dept Chemistry, Univ. Colo.; Dept. Chemistry, University of TexasThe conversion of peroxyl radicals to organic nitrates via reaction with NO is of importance in atmospheric chemistry and biochemistry. The mechanism for nitrate formation is obscure; no previous theoretical results have been even vaguely consistent with the experimental evidence. We propose a simple valence bond argument to rationalize how an initially formed pernitrite, ROONO, can decompose to an alkoxy radical and $NO_{2}$ or rearrange to $RONO_{2}$. This qualitative mechanism, which involves the coupling of two valence bond states, is supported by coupled-cluster electronic structure calculations that predict a barrier of ca. 20-30 kcal $mol^{-1}$, that is provided by the radical/radical adduct. In addition to its obvious importance for atmospheric chemistry, it is likely that this mechanism is also responsible for chain termination of the oxygen-dependent oxidation of lipid membranes in biological cells. The mechanism can likewise be applied to the thermal decomposition of organic nitro compounds (explosives and solid propellants), $RNO_{2} + heat \rightarrow$ products