0 12 3 456 4714 - Université Grenoble Alpespanchish/moscou201211/moscou201211-v2.pdf/&)0!)%0&!...
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Transcript of 0 12 3 456 4714 - Université Grenoble Alpespanchish/moscou201211/moscou201211-v2.pdf/&)0!)%0&!...
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∫Z
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%& @%="+
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}+
"
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>
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θ(δ)(H+ &))µ())
)- 5 2"5&/#" µ )+ Z∗
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&"#%"& 0θ,µ(&) =∑
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1
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G (!"#" (H+ &)) =∑
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#
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0−
"
∈ Q, (" ≥ 8 )2)$ )
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: %!
→ C!
<=')") %
!
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= &'(
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+"#$3*!".
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())
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− !
∈ %
!
4 =')") C!
= Q̂!
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4 ) ∈ %
!
<# C!
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!
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(+ + !
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)
=
[ '
!
"
]+ −
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=
,
({ '
!
"
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!
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)*#04"* µ
/-*"* θ (0 # 6-#"#6+*" )!& 7
!θ, (") :=
∫
Z∗
θ(#)χ(!)(〈#〉)µ
=∞∑
"=
$
"
"
" ∈ Z#
[["]], #$&
χ(!) : (8+ )$ 7→ (8+ ")$ , 〈#〉 = #
ω(#), ω +-* 9*(6-):;;*"
6-#"#6+*"< 2#34"50 ($+*="#; !1 +-* 6-#"#6+*" #
%−! = ω%−! · χ(!)0-!/0 +-#+ θ = ω%−!, (8+ ") = (8+ )%−!
ζ(8− %)(8−
%−!) =!θ, ((8+ )%−! − 8)
8− &
%
. >?@
A% +-* B*(*"0+"#00 '"*'#"#+(!$ +-*!"*) /* -#C* # &*6!)'!0(+(!$
!θ, (") = 'θ, (")(θ, (")
/(+- # &(0+($=4(0-*& '!;%$!)(#; (θ, (") #$& ($C*"+(D;* '!/*" 0*"(*0'θ, (")< 9-* ($C*"0(!$ !1 >?@ 1!" #$% *C*$ % ≥ E =(C*0 F
8
ζ(8− %)(8−
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%).
!
!" #$%&"'( )*' #$+ ,'-." > / #$0 "1"$ ! ≥ /
! "#$ %&''&( )* +(,!,(, %-)." &) &) =
= (/ + !) − / 0 1 0$0
23 , 0 !" )*-!#$0 4&'3)&5 ,'6
/
ζ(/− ")(/− !
− )=
#
∗θ,!((/ + !) − − /)(/− $
)
%θ,!((/ + !) − − /)789
=#
∗θ,!((/ +
)(/ + !)− − /)(/− $
)
%θ,!((/ +
)(/ + !)− − /)
(# .# ! 5$:&5&:4# . ) "#$ -) " 0 !. &% "#$ 1,: ,2'$
= (/ + !) − / ( "# , ;) "$ )-52$: &% 4&'$! 7$<4:$!!$0 1 , :&&"!
&% %θ,!9 %&: θ = ω − = ,)0
#
∗θ,!((/ + !) − − /) := //#θ,!((/ + !) − − /).
>#$ ,2&1$ %&:5-', 55$0 ,"$'3 $<"$)0! "& ,'' ? : .#'$" &@%-)." &)!
&% .#,:,."$:! χ 5&0 !
"
,! "#$ %&''&( )* +(,!,(, %-)." &) 0 1 0$0
23 , 4&'3)&5 ,'6
/
&(/− " , χ)(/− χ(!)! − ) =#
∗θ,!(χ(/ + !)(/ + !) − − /)(/− χ($)$ )
%θ,!(χ(/ + !)(/ + !) − − /)
(#$:$
#
∗θ,!(χ(/ + !)(/ + !) − − /) := /
#θ,!(χ(/ + !)(/ + !) − − /)
2334%5'#5-*$( $4."'-6#3 1#34"% *) ζ(7− /!)− (7−
! − )−
)*' = 89
*4 A !"#$%&$'()* +,-(.&/!0(10#2&,-()-&%+$3&,-(+%)45&$36)))7
*4 A 4BCDE
*4 A %&:7FB/=74@/9GH= 4: )"7HIF= J$",4/74=F999
H" ζ(/− H")− (/− !
! − )−
H H8 + HK ∗ CD + HK ∗ CD
! + HK ∗ CD
" + HK ∗ CD
# + '(CD
$)
K L + C ∗ CD + L ∗ CD
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# + '(CD
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M D + CN ∗ CD + CM ∗ CD
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# + '(CD
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O /O + M ∗ CD + '(CD
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/N /M + CC ∗ CD + CM ∗ CD
! + CM ∗ CD
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/H O + H8 ∗ CD + HO ∗ CD
! + HC ∗ CD
" + '(CD
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/K H8 + CM ∗ CD + CM ∗ CD
! + CM ∗ CD
" + CM ∗ CD
# + '(CD
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/M M + /M ∗ CD + C/ ∗ CD
! + HL ∗ CD
" + HN ∗ CD
# + '(CD
$)
/O C + K ∗ CD + /N ∗ CD
! + CH ∗ CD
" + H8 ∗ CD
# + '(CD
$)
HN // + /C ∗ CD + /L ∗ CD
! + CM ∗ CD
" + /H ∗ CD
# + '(CD
$)
HH / + HM ∗ CD + /8 ∗ CD
! + C8 ∗ CD
" + L ∗ CD
# + '(CD
$)
HK /M + HO ∗ CD + HK ∗ CD
! + HD ∗ CD
" + C/ ∗ CD
# + '(CD
$)
HM K + /D ∗ CD + H8 ∗ CD
! + H8 ∗ CD
" + /L ∗ CD
# + '(CD
$)
HO HH + CM ∗ CD + O ∗ CD
! + K ∗ CD
" + CC ∗ CD
# + '(CD
$)
CN HH + 8 ∗ CD + C8 ∗ CD
! + L ∗ CD
" + 8 ∗ CD
# + '(CD
$)
CH CM ∗ CD
− + HO + C ∗ CD + /L ∗ CD
! + /O ∗ CD
" + '(CD
#)
CK HN + CD + CN ∗ CD
! + /8 ∗ CD
" + HH ∗ CD
# + '(CD
$)
CM CM ∗ CD + HL ∗ CD
! + C8 ∗ CD
" + 8 ∗ CD
# + CD
$ + '(CD
%) !
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# $/' )$-&(/-!#&'"+ !-) :5G&$4 $'$' >G&$HFA 3!.$ ! "/(<2/1$)
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