Read e-book online Automorphic forms on GL(2) PDF

By H. Jacquet, R. P. Langlands

ISBN-10: 3540059318

ISBN-13: 9783540059318

Show description

Read Online or Download Automorphic forms on GL(2) PDF

Best algebra books

Download e-book for kindle: Exploratory Galois Theory by John Swallow

Combining a concrete viewpoint with an exploration-based process, this research develops Galois thought at a wholly undergraduate point.

The textual content grounds the presentation within the inspiration of algebraic numbers with complicated approximations and basically calls for wisdom of a primary path in summary algebra. It introduces instruments for hands-on experimentation with finite extensions of the rational numbers for readers with Maple or Mathematica.

Download e-book for iPad: Elements of the Representation Theory of Associative by Assem I., Simson D., Skowronski A.

This primary a part of a two-volume set deals a contemporary account of the illustration concept of finite dimensional associative algebras over an algebraically closed box. The authors current this subject from the point of view of linear representations of finite-oriented graphs (quivers) and homological algebra.

Get Scissors Congruences, Group Homology & C PDF

A set of lecture notes in keeping with lectures given on the Nankai Institute of arithmetic within the fall of 1998, the 1st in a chain of such collections. specializes in the paintings of the writer and the past due Chih-Han Sah, on facets of Hilbert's 3rd challenge of scissors-congruency in Euclidian polyhedra.

Read e-book online Computational Algebra and Number Theory PDF

Desktops have stretched the boundaries of what's attainable in arithmetic. extra: they've got given upward push to new fields of mathematical research; the research of latest and conventional algorithms, the construction of recent paradigms for enforcing computational tools, the viewing of outdated options from a concrete algorithmic vantage aspect, to call yet a number of.

Additional info for Automorphic forms on GL(2)

Sample text

Let V be the space on which the Kirillov model of π acts. For every W in W (π, ψ) there is a unique ϕ in V such that W a 0 0 1 = ϕ(a). Chapter 1 39 If π is itself the canonical model π(w)ϕ(a) = W where a 0 0 1 0 1 −1 0 w= w . If χ is any quasi-character of F × we set ϕ(a)χ(a) d× a ϕ(χ) = F× if the integral converges. If χ0 is the restriction of χ to UF then ϕ(χ) = ϕ χ0 , χ( ) . Thus if αF is the quasi-character αF (x) = |x| and the appropriate integrals converge s−1/2 ) = ϕ(1, q 1/2−s ) s−1/2 ω −1 ) = ϕ(ν0−1 , z0−1 q 1/2−s ) Ψ(e, s, W ) = ϕ(αF Ψ(e, s, W ) = ϕ(αF if ν0 is the restriction of ω to UF and z0 = ω(ϕ).

Let F be the space of continuous functions f on GF which satisfy a1 x 0 a2 f g = a1 f (g) a2 1/2 −1/2 for all g in GF , a1 , a2 in F × , and x in F . We observe that F contains B(αF , αF The Haar measure on GF if suitably normalized satisfies f (g) dg = GF NF AF GL(2,OF ) if a1 0 0 a2 a= a1 a2 ). GF acts on F. −1 f (nak) dn da dk . It follows easily from this that f (k) dk GL(2,OF ) is a GF -invariant linear form on F. There is also a positive constant c such that f (g) dg = c GF NF AF NF a1 a2 −1 f na 0 1 −1 0 n1 dn da dn1 .

10 we see that all of the sequences satisfying the recursion relation p λa ϕn−i (µ) ϕn (µ) = i=1 for n ≥ n1 . The integer n1 depends on ϕ. 1 is therefore a consequence of the following elementary lemma whose proof we postpone to Paragraph 8. 4 Let λi , 1 ≤ i ≤ p, be p complex numbers. Let A be the space of all sequences {an }, n ∈ Z for which there exist two integers n1 and n2 such that an = λi an−i 1≤i≤p for n ≥ n1 and such that an = 0 for n ≤ n2 . Let A0 be the space of all sequences with only a finite number of nonzero terms.

Download PDF sample

Automorphic forms on GL(2) by H. Jacquet, R. P. Langlands

by Steven

Rated 4.17 of 5 – based on 10 votes