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
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