Publisher description
The authors determine the number of level $1$, polarized, algebraic regular, cuspidal automorphic representations of $\mathrm{GL}_n$ over $\mathbb Q$ of any given infinitesimal character, for essentially all $n \leq 8$. For this, they compute the dimensions of spaces of level $1$ automorphic forms for certain semisimple $\mathbb Z$-forms of the compact groups $\mathrm{SO}_7$, $\mathrm{SO}_8$, $\mathrm{SO}_9$ (and ${\mathrm G}_2$) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the $121$ even lattices of rank $25$ and determinant $2$ found by Borcherds, to level one self-dual automorphic representations of $\mathrm{GL}_n$ with trivial infinitesimal character, and to vector valued Siegel modular forms of genus $3$. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy
More books by the authors
Similar books
Rate the book
Write a review and share your opinion with others. Try to focus on the content of the book. Read our instructions for further information.
Level One Algebraic Cusp Forms of Classical Groups of Small Rank
Book reviews » Level One Algebraic Cusp Forms of Classical Groups of Small Rank
|
|
![Level One Algebraic Cusp Forms of Classical Groups of Small Rank](/images/background.gif) |
![Level One Algebraic Cusp Forms of Classical Groups of Small Rank](/images/background.gif) |
|
|
|