''Automorphic Forms on GL(2)'' is a mathematics book by where they rewrite
Erich Hecke
Erich Hecke (20 September 1887 – 13 February 1947) was a German mathematician known for his work in number theory and the theory of modular forms.
Biography
Hecke was born in Buk, Province of Posen, German Empire (now Poznań, Poland). He o ...
's theory of
modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory ...
s in terms of the
representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
of GL(2) over
local field
In mathematics, a field ''K'' is called a (non-Archimedean) local field if it is complete with respect to a topology induced by a discrete valuation ''v'' and if its residue field ''k'' is finite. Equivalently, a local field is a locally compa ...
s and
adele ring
Adele Laurie Blue Adkins (, ; born 5 May 1988), professionally known by the mononym Adele, is an English singer and songwriter. After graduating in arts from the BRIT School in 2006, Adele signed a reco ...
s of
global field In mathematics, a global field is one of two type of fields (the other one is local field) which are characterized using valuations. There are two kinds of global fields:
*Algebraic number field: A finite extension of \mathbb
*Global function fi ...
s and prove the
Jacquet–Langlands correspondence. A second volume by gives an interpretation of some results by Rankin and Selberg in terms of the representation theory of GL(2) × GL(2).
References
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External links
*{{citation, url=http://wwwf.imperial.ac.uk/~buzzard/maths/research/notes/summary_of_first_bit_of_jacquet_langlands.pdf, last=Buzzard, first=Kevin, title=What is in the book ''Automorphic forms on GL(2)'' by Jacquet and Langlands?, year=2012
Langlands program
Representation theory
Mathematics books