Invariants, cohomology, and automorphic forms of higher order

Details Invariants, cohomology, and automorphic forms of higher order Invariants, cohomology, and automorphic forms of higher order

2008-11-07

arxiv.org/abs/0811.1088v3

Mathematics

Number Theory

Selecta Mathematica 2012. arXiv admin note: substantial text overlap with arXiv:0805.0703

Scientific paper

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and a higher order version of Borel's conjecture is stated.

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