УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÔØÖºÓÒ<strong>×</strong>ØÖÙØÒØÅÓÙÐÖÓÖÑ<strong>×</strong><br />
´º½½µ<br />
ÜÔÒ<strong>×</strong>ÓÒÓØÂÓÓÖÑÒÓÛÒÚÓÐÚ<strong>×</strong>йÒØÖÐÜÔÓÒÒØ<strong>×</strong>ºÇÒ<strong>×</strong><br />
(Z)ÚØØÚÐغÌÓÙÖÖ<br />
<strong>×</strong>ÒÜÑÔиØÂÓÓÖÑÓÛØ5ÒÒÜ1/2<br />
ÒÖØ<strong>×</strong>ØËÐÑÓÙÐÖÓÖÑÛØÖØÖ¸∆ 5<br />
(Z)<strong>×</strong>ØÓÐÐÓÛÒÜÔÒ<strong>×</strong>ÓÒ℄ ´º½¾µ<br />
ÆÓØØ<strong>×</strong>ÑÐÖØÝÛØØÅÓÖÑÙÐÚÒÒÕº´ºµÛØйÒØÖÐÔÓÛÖ<strong>×</strong>Óq¸ ´º½¿µ<br />
≥ 0ºÌÑÓÙÐÖÓÖÑ∆ rÒsÔÔÖÒÛÖÒØÖÐÔÓÛÖ<strong>×</strong>ÔÔÖºÖØ<strong>×</strong>ÒÓÒÆÙÐÒÚ<strong>×</strong>ÓÛÒØØ<br />
, l d d)<br />
q n/2 r l/2 s m/2 . 2<br />
Z)ºÁØØÖÒ<strong>×</strong>ÓÖÑ<strong>×</strong><strong>×</strong> ´º½µ<br />
Ø<strong>×</strong>ÑÓÙÐÖÓÖÑÔÔÖ<strong>×</strong><strong>×</strong>ØÒÓÑÒØÓÖÓÖÑÙÐÓÃÅÄ<strong>×</strong>ÙÔÖÐÖº∆ 5<br />
<strong>×</strong>ÑÓÙÐÖÓÖÑÛØÖØÖÙÒÖØÙÐÐÑÓÙÐÖÖÓÙÔ¸Sp(2,<br />
(M)<strong>×</strong>℄ ´º½µ<br />
ÛÖvΓ (M)<strong>×</strong>ØÙÒÕÙÒÓÒ¹ØÖÚÐÖÐÐÒÖÖØÖÓSp(2, Z)¼℄ÒM =<br />
Sp(2, Z)ºÒÜÔÐØÜÔÖ<strong>×</strong><strong>×</strong>ÓÒÓÖv = (−1) b 1+b 2 +b ,<br />
= (−1) (1+u 0+u 2 )(1+u 1 +u 3<br />
)<strong>×</strong>ÙÒ¹ÑÓÙÐÖÑØÖܺ ´º½µ<br />
)+u 0 u 2<br />
,<br />
ÁÒÔØÖ2¸ÛÓÙÒØØ<strong>×</strong>ØØ<strong>×</strong>ÓØÐÓÐÜÔÐØÐÝØÓÓØÒØÙÐÐÔÖØØÓÒ º¿ ÛÖI 2<strong>×</strong>Ø2 ÌØÚ<strong>×</strong>ÓÖÀÄÑÓÐ<strong>×</strong><br />
)ÒU <strong>×</strong> 2ÒØØÝÑØÖܸB=<br />
b b 2 u 1 u<br />
4¹ÈË<strong>×</strong>ØØ<strong>×</strong>ºÏ<strong>×</strong>ÛØØØÓÙÒØÒ¸ÒÒØÔÖØØÓÒÙÒØÓÒ¸½<br />
2<br />
ÙÒØÓÒÓØ1<br />
ÛØg(n, l) = 0ÙÒÐ<strong>×</strong><strong>×</strong>4n−l<br />
2<br />
∆ 5 (Z) =<br />
ψ 5,1/2 (z 1 , z 2 ) = ϑ 1 (z 1 , z 2 ) η(z 1 ) 9 ,<br />
ψ 5,1/2 (z 1 , z 2 ) =<br />
∑<br />
(n,l,m)>0<br />
Γ<br />
∑<br />
n,l=1ÑÓ2<br />
5<br />
∑<br />
d|(n,l,m)<br />
d k−1 g ( nm<br />
g(n, l) q n/2 r l/2 ,<br />
∆ 5 (M · Z) = v Γ (M) (CZ + D) 5 ∆ 5 (Z) ,<br />
( ) ( )<br />
v Γ 0 −I 2<br />
= 1 , v Γ I 2 B<br />
I 2 0 0 I 2<br />
( )<br />
v Γ U T 0<br />
0 U 1 ( b 1 b<br />
=<br />
( u 0 u 3<br />
(Z)<br />
( A B<br />
C D ) ∈
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