Index
a, 171
a x , 43
a
r
, 215
a
c
, 215
Bm(x), 16
B(p,q), 63
B(
X
i,X2),222
Cf, 52
Cl(A),Cl,jtk(A),22
e
a
(*), 172
£ ( # , / ) , 218
£*.(*, s; A), 171
£
x
(z,s;a) , 175
^ 178^
G, G+, G_, 74
G(c), 78, 85
0K(id,r),
5 / f
( i d , T ; { C j } j

j , a J , 79
fl'K/F(id,r;{Cj}J-ej,aM), 89
^
}
( i d , r ) , 251
7fe, 169
7fc(c), 170
lf ] (z,u;), 16
r
r
(x,a;) (=ri
1 ]
(x,a;)), 16
h, 171
/i
x
(z;a), 176
A
r
(a,b,£) , 27
PK(C,ry), 62
R(Cj,c), 53
fl(X,/),44
p[?](x,u;), 15
/9r(x,u;) (= p\r](x,ou)), 16
5 ( ^ ) , S(£A), 234
Tw, 222, 242
V(c), 79, 85
W(c), 79, 85
X W J f q ^ ^ j ^ J , 79
X^iclCjjjej,a^), 257
£(0,/i;a,/3), 172
C F ( S , C ) , 5 2
£r(s,u;,;c), 13
C(s,A,x), 17
analytic class number formula, 43
absolute period symbol, 79
Artin's unit theorem, 46
asymptotic expansion of the r-ple gamma
function, 35
Bernoulli polynomial, 16
beta function, 63
big cell, 147
big cone, 147
Chowla-Selberg formula, 63, 74
real case, 126
cone decomposition, 52
confluent hypergeometric function, 172
Conjecture A=Conjecture III, 3.2, 75
Conjecture B=Conjecture III, 3.9, 81
Conjecture C=Conjecture III, 3.10, 83
Dedekind //-function, 178
exact Chowla-Selberg formula, 184
generalization of, 183
Eisenstein series, 171, 218
face, 136
Fermat curve, 65
fine sequence, 149
generalized regulator, 44
Hurwitz's zeta function, 17
K-Bessel function, 173, 227
Kronecker's first limit formula, 178
lattice, 179
Liouville's theorem, 38
limit formula of Kronecker's type, 177
non-degenerate CM-type, 270
odd representation, 74
open simplex, 135
open simplicial cone, 52
order of an algebraic number field, 189
Poisson summation formula, 236
precise form of Stark's conjecture, 50
primitive CM-type, 269
proper ideal, 189
rank of a CM-type, 270
reciprocity map, 83
refinement, 84
reflex, 270
r-ple Riemann zeta function, 13
r-ple gamma function, 16
Schwartz-Bruhat function, 171, 234
self-dual measure, 236
Shimura's period symbol, 62
Shimura's reciprocity law, 205
Shintani's formula
for C(0,A,x), 20
for C(0,A,x), 23
281
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