Electron spin resonance investigation of carbon-13 hyperfine interactions in nitrobenzene anion radical

Synthesis of carbon-13 enriched nitrobenzene which contains 22·5 mole per cent of nitrobenzene-1-¹³C and an equal amount of nitrobenzene-4-¹³C has been accomplished. We report the carbon-13 hyperfine interactions in the corresponding anion radicals in a variety of solvent media. In hexamethylphosphoramide a _C1 = -7·05 gauss and a _C4 = 6·14 gauss. These couplings change to -9·03 gauss and 5·31 gauss, respectively, when the solvent medium is dimethylformamide containing 0·598 mole fraction of water. The solvent dependence of a _C1 is consistent with the radical remaining planar as opposed to adopting a pyramidal conformation at the nitrogen when hydrogen bonds form between the radical anion and protic solvents. Data reported here provide an experimental means to estimate the spin density distribution in nitrobenzene anion.     

Arsen, Antimon

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Converse theorems assuming a partial euler product

Associated to a newform f(z) is a Dirichlet series L _f (s) with functional equation and Euler product. Hecke showed that if the Dirichlet series F(s) has a functional equation of a particular form, then F(s)=L _f (s) for some holomorphic newform f(z) on Γ(1). Weil extended this result to Γ₀(N) under an assumption on the twists of F(s) by Dirichlet characters. Conrey and Farmer extended Hecke’s result for certain small N, assuming that the local factors in the Euler product of F(s) were of a special form. We make the same assumption on the Euler product and describe an approach to the converse theorem using certain additional assumptions. Some of the assumptions may be related to second order modular forms. This work resulted from an REU at Bucknell University and the American Institute of Mathematics. Research supported by the American Institute of Mathematics and the National Science Foundation.