Index

abelian L-functions, 93

abelian L-function, 60

absolute Weil group, 84

adele group /CA 39

adelized discriminant, 182

admissible representation, 62

Artin-Hecke L-function, 100

automorphic representation, 68

Bohr compactification, 213

characters, 6

conductor of a representation, 89

constant term, 245

decomposition group, 94

Delsart's explicit formula, 151

digamma function, 159

Dirac distribution, 10

discretely modulated groups, 80

dual group, 4, 109

duality theory, 3

elementary, 77

elementary character, 86

elementary group, 8

explicit formula for Artin-Hecke

L-functions, 174

explicit formula for Automorphic

L-functions, 175

exponent, 23

finite value, 35

first kind, 96

Fourier inversion formula, 4

Probenius element, 80

Functional Equation, 60

functional equation, 101

fundamental principle, 183

growth exponent, 119

Haar measure, 2

Hecke L-function, 59

idele group, 43

infinitesimally equivalent, 105

Langlands class, 111

Langlands L-group, 110

local functional equation, 18

local Langlands' correspondence, 103

locally compact, 1

logarithmic integral, 144

modulated group, 80

Peter-Weyl Theorem, 216

Poisson summation formula, 13

Poisson type, 12

Pontrjagin Duality, 4

positive definite, 211

prime character, 74, 86

primitive, 74

principal value, 158, 160

quasi-character, 6

regulator, 51

relative invariant measure, 3

restricted direct product, 5

Riemann's explicit formula, 145

Riemann's product formula, 120

Root Number, 32

Schwartz-Bruhat function, 8

second kind, 96

self-dual measure, 4

support of a distribution, 10

tempered distributions, 9

topological group, 2

Tychonoff topology, 1

unramified, 63

Von Mangoldt's explicit formula, 147

Whittaker functions, 64

zeta function, 18

idele, 43