This article analyzes the electronic factors governing bond length alternation (BLA) in linear polyenes. The impact of various effects is illustrated on small all-trans polyenes, namely butadiene, hexatriene and octatetraene prototype molecules. It well known that self-consistent-field single determinant treatments overestimate paper aims to identify physical correlation which correct this defe...

A strong impetus for this paper came, at least for the first author, from a question of Avner Ash, asking whether one can construct non-self-dual, nonmonomial cuspidal cohomology classes for suitable congruence subgroups Γ of SL(n,Z), say for n = 6. Such a construction, in special examples, has been known for some time for n = 3 (see [2, 34, 35, 36]); it is of course not possible for n = 2. One...

A fundamental problem in number theory is to estimate the values of L-functions at the center of the critical strip. The Langlands program predicts that all L-functions arise from automorphic representations of GL(N) over a number field, and moreover that such L-functions can be decomposed as a product of primitive L-functions arising from irreducible cuspidal representations of GL(n) over Q. T...