 
Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & SpringerVerlag
Zbl 1161.11009
Jiang, Dihua
Periods of automorphic forms. (English)
Chen, Zhijie (ed.) et al., Proceedings of the international conference on complex geome
try and related fields, Shanghai, China, 2004. Providence, RI: American Mathematical
Society (AMS); Somerville, MA: International Press. AMS/IP Studies in Advanced
Mathematics 39, 125148 (2007). ISBN 9780821839492/pbk
This paper surveys some aspects of the theory of periods of automorphic forms on a
reductive group. A period of an automorphic form on G is essentially its integral over
a subgroup H. Automorphic representations admitting a nonvanishing period integral,
the so called distinguished representations, are of considerable interest. For instance,
nonvanishing of the period integral is related to functoriality in certain contexts and in
some situations it is related to special Lvalues. The local analogue of this notion is
expressed in terms of the existence of a nontrivial invariant linear form on the space
of the local representation. The global condition ensures that the local criterion is
met at all the places. One can ask when will, and under what extra assumptions, the
local period condition guarantees the global nonvanishing. The paper discusses all these
points with a lot of examples.
