Invariants, cohomology, and automorphic forms of higher order
نویسندگان
چکیده
منابع مشابه
ov 2 00 8 Higher order invariants , cohomology , and automorphic forms Anton
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 ...
متن کامل7 N ov 2 00 8 Higher order invariants , cohomology , and automorphic forms
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 ...
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In this paper a theory of Hecke operators for higher order modular forms is established. The definition of higher order forms is extended beyond the realm of parabolic invariants. A canonical inner product is introduced. The role of representation theoretic methods is clarified and, motivated by higher order forms, new convolution products of L-functions are introduced.
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In this paper, we construct an explicit basis for modular forms of all orders. Higher order modular forms are a natural generalization of the classical concept of automorphic forms, and have been to attracting increasing interest in recent years. They have proved to be relevant to problems related to the distribution of modular symbols ([CDO]), to GL(2) L−functions ([DKMO],[FW]), to percolation...
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In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic methods is clarified and, motivated by higher order forms, new convolution products of L-functions are introduced.
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2012
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-012-0087-1