There are two well-known L-functions attached to Siegel modular forms of degree two. These are the Spin and the standard L-function. They have been studied by Andrianov, Böcherer, Shimura, and o...
Consider the Lie group defined as where Its Lie algebra is the set of all matrices with real entries such that A general element of is of the form and so is a 21-dimensional real vector space. We...
Let be a smooth projective variety of genus over . Arithmetic information about the curve is encoded in its L-function . The conjectures of Birch and Swinnerton-Dyer about elliptic curves over we...
One of the motivations of studying the Langlands Conjectures is the question What are the finite extensions of the rational numbers? The local Langlands Conjectures give a dictionary between the ...
https://automorphicforum.wordpress.com/2012/02/07/lectures-on-the-langlands-conjectures/
Let be a connected reductive group over a nonarchimedean field and let be congruences subgroup of . Let be an irreducible smooth admissible representation of . Suppose is supercuspidal and . Then...
Jacquet and Langlands have shown how to associate classical holomorphic modular forms f to automorphic representations of . These representations can be written in terms of local components. In t...
https://automorphicforum.wordpress.com/2012/01/11/the-paramodular-conjecture/
Today I want to talk about a paper by Dick Gross, where he describes how to attach a motive of Artin-Tate type to a connected reductive group over a field . The motive and its -function are parti...
https://automorphicforum.wordpress.com/2011/10/08/motives-of-reductive-groups/
Let and let be the nilpotent radical of the standard Borel subgroup, i.e., is the subgroup of consisting of upper triangular matrices with 1’s on the diagonal. Given a non-trivial character , w...
https://automorphicforum.wordpress.com/2011/08/07/gelfand-graev-representations/
I have been reading “Number Theory I: Fermat’s Dream” by Kazuya Kato, Nobushige Kurokawa, and Takeshi Saito. In Chapter 1: Rational Points on Elliptic Curves, the authors state two proposit...
https://automorphicforum.wordpress.com/2011/02/01/elliptic-curves-and-fermats-last-theorem-for-n4k/
The following is taken from notes distributed by Matthew Morrow at the Midwest Number Theory Conference for Graduate Students and Recent PhD’s 2010: A two-dimensional local field F is a complet...
https://automorphicforum.wordpress.com/2010/12/08/two-dimensional-adelic-analysis/