Results 161 to 170 of about 11,043,146 (220)

Automorphic Forms

, 2015
Salvatore Mercuri, Kevin Buzzard
semanticscholar   +2 more sources

Coherent cohomology of Shimura varieties and automorphic forms

Annales Scientifiques de l'Ecole Normale Supérieure, 2018
We show that the cohomology of canonical extensions of automorphic vector bundles over toroidal compactifications of Shimura varieties can be computed by relative Lie algebra cohomology of automorphic forms.
Jun Su
semanticscholar   +1 more source

Automorphic Forms on the Stack of G-Zips

Results in Mathematics, 2018
We define automorphic vector bundles on the stack of G-zips introduced by Moonen–Pink–Wedhorn–Ziegler and study their global sections. In particular, we give a combinatorial condition on the weight for the existence of nonzero mod p automorphic forms on ...
Jean-Stefan Koskivirta
semanticscholar   +1 more source

Smooth-Automorphic Forms and Smooth-Automorphic Representations

2021
This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider "K-finite" automorphic forms, but we allow a richer class ...
openaire   +2 more sources

Converse theorems for automorphic distributions and Maass forms of level N

Research in Number Theory, 2019
We investigate the relationship between L-functions satisfying certain functional equations, summation formulas of Ferrar–Suzuki type and Maass forms of integral and half-integral weight.
T. Miyazaki, Fumihiro Sato, K. Sugiyama, T. Ueno   +3 more
semanticscholar   +1 more source

On a strange invariant bilinear form on the space of automorphic forms

, 2015
Let F be a global field and $$G:=SL(2)$$G:=SL(2). We study the bilinear form $${{\mathcal {B}}}$$B on the space of K-finite smooth compactly supported functions on $$G({\mathbb {A}})/G(F)$$G(A)/G(F) defined by $$\begin{aligned} {{\mathcal {B}}}(f_1,f_2):=
V. Drinfeld, Jonathan Wang
semanticscholar   +1 more source

Classical Automorphic Forms

2004
With automorphic forms and their associated L-functions, one enters into new territory; the catch-phrase here is that we will describe the GL(2) analogue of the GL(1) theory of Dirichlet characters (i.e., over Q). The corresponding work for more general groups and general base field K will be described in later chapters.
openaire   +1 more source

Primitive Automorphic Forms

2001
There seems to be a marvellous interaction taking place between mathematical physics and mathematics in the area of geometry, demanding a greater contribution from non-commutative structures and higher cohomologies. It may require a revolutional extension of the concept of spaces in order to explain the dualities there.
openaire   +1 more source

Singular Automorphic Forms

1995
In the context of holomorphic forms on tube domains, singular automorphic forms were studied by Maass [Maa], Freitag [Fre], and Resnikoff [Res], among others. A holomorphic form is singular if it is annihilated by certain differential operator(s). It is known that this is the case if and only if all its “nondegenerate” Fourier coefficients vanish, and ...
openaire   +1 more source

Rigidity for automorphic forms

Journal d'Analyse Mathématique, 1987
For a general reductive group G, the multiplicity one theorem fails, but there is hope for the following ``global rigidity conjecture'': given an automorphic \(\pi =\otimes \pi_{\nu}\) and a finite set of places V, there are only finitely many automorphic \(\pi '=\otimes \pi '_{\nu}\) with \(\pi_{\nu}\) equivalent to \(\pi '_{\nu}\) for \(\nu\) outside
openaire   +1 more source