УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÔØÖºÅÓÙÐÖÓÖÑ<strong>×</strong> nÓÖ<strong>×</strong>ÓÑ<br />
ÓÒØÓÒÓÖØÛÓÐÑÒØ<strong>×</strong>ÓMØÓÓÖÖ<strong>×</strong>ÔÓÒØÓØ<strong>×</strong>ÑÐØØÒLØÙÖÒ<strong>×</strong>ÓÙØØØØÝ<br />
2}ÓMÓÖÖ<strong>×</strong>ÔÓÒØÓØ<strong>×</strong>ÑÐØØÒLÌÒ<strong>×</strong><strong>×</strong>ÖÝÒ<strong>×</strong>ÙÒØ<br />
)¸ÛÛÓÙÐÐØÓ<strong>×</strong>ÛÒÓØÛÓ<strong>×</strong>ÙÔÖ<strong>×</strong> ÓØÒÝÒØÝÒØÔÓÒØ<strong>×</strong>z Z)ºÌÙ<strong>×</strong>¸Û<strong>×</strong>ØØÛÒÒØÝØ<strong>×</strong>ØLÓÐØØ<strong>×</strong><br />
1 , z 2 ∈ C<strong>×</strong>ÙØØz 1 − z 2 = ω 1 m + ω 2<br />
ÆÓÛ¸ÚÒM¸Ø<strong>×</strong>ØÓÐÐÔÖ<strong>×</strong>(ω 1 , ω 2<br />
{ω 1 , ω 2 }Ò{ω<br />
)ÓM´Ö<strong>×</strong>ÔØÚÐÝLµ<strong>×</strong>ÓÐÐÓÛ<strong>×</strong><br />
1, ω ∗ÓÒÒÝ<br />
′<br />
<strong>×</strong>ÓÙÐÓÒÖÙÒØÑÓÐÙÐÓSL(2,<br />
´º¿½µ<br />
ÓCÛØØÕÙÓØÒØÓMÝØØÓÒÓSL(2, Ð<strong>×</strong>Ó¸<strong>×</strong>ÒØ<strong>×</strong>ÓÒÐÝØÖØÓØØØÖÑÒ<strong>×</strong>ØÐØظÛÒØÝC ÐÑÒØ(ω 1 , ω<br />
ÓΓ(1)ÓÒHºÏÑØ<strong>×</strong>ÔÖÐÓÛ¸ÛÖÛÜÔÐÒÛØÛ<strong>×</strong>ÒØ<br />
2<br />
(ω 1 , ω 2 ) ↦→ (λω 1 , λω 2<br />
Z)ÓÒMÒØÓØØ<br />
), (Ö<strong>×</strong>ÔºL λL), λ ∈ C ∗ ,<br />
ÛØÓÙØÒÒØÖØÓºÌÙ<strong>×</strong>¸ÛÒÒØÝØÕÙÓØÒØM/C<br />
ÓΓ(1)\HÛØÐØØÓCÙÔØÓÓÑÓØØÝ´ÐØÓÒµº ÒÒÒÓÙØØÒØØÓÒÓÐØØÓCÛØØÕÙÓØÒØH/Γ(1)ºÌÑÔ<br />
∗ÛØHÝ(ω 1 , ω 2 ) ↦→<br />
z = ω 1 /ω 2¸ÒØÙ<strong>×</strong>¸Ø<strong>×</strong>ÒØØÓÒØÖÒ<strong>×</strong>ÓÖÑ<strong>×</strong>ØØÓÒÓSL(2,<br />
Z¸Û<strong>×</strong>ÝØØÓÑÔÐÜÚÐÙÙÒØÓÒ¸F¸ÓÒL<strong>×</strong>ÓÛØk<br />
∗ÓÒØÓΓ(1)\HºÌÙ<strong>×</strong>¸ÛÒÒØÝÒÐÑÒØ<br />
(ω 1 , ω 2 ) ↦→ ω 1 /ω 2Ú<strong>×</strong>ØÓÒÓL/C<br />
´º¿¾µ ÓÖk∈<br />
)ºÌÒØÓÚÓÖÑÙÐ<strong>×</strong>Ù<strong>×</strong>Ø<br />
)ØÚÐÙÓFÓÒØÐØØ<br />
F(λL) = λ −k F(L)<br />
ÓÖÐÐÐØØ<strong>×</strong>L∈LÒÐÐλ ∈ C ∗ºÄØÙ<strong>×</strong>ÒÓØÝF(ω , ω 2<br />
´º¿¿µ<br />
L(ω<br />
ÌÙ<strong>×</strong>¸ÛÒÐÛÝ<strong>×</strong>ÒÙÒØÓÒ¸f¸ÓÒH<strong>×</strong>ÙØØ<br />
1 , ω 2<br />
ÏÒÓØÒØÓÚÓÖÑÙÐØØØÔÖÓÙØω<br />
Z)ØÓÒÓÒM¸Û<strong>×</strong>ØØf<strong>×</strong>Ø<strong>×</strong><strong>×</strong>Ø<br />
2 −k F(ω 1 , ω 2<br />
´º¿µ<br />
)ÔÒ<strong>×</strong>ÓÒÐÝÓÒz 2 f(ω 1/ω 2 )<br />
Ð<strong>×</strong>Ó¸<strong>×</strong>ÒF(ω 1 , ω 2 )<strong>×</strong>ÒÚÖÒØÙÒÖÒSL(2, ½¾<br />
m, n ∈ Zº<br />
′<br />
↦→<br />
1<br />
F(λω 1 , λω 2 ) = λ −k F(ω 1 , ω 2 ) .<br />
F(ω 1 , ω 2 ) = ω −k<br />
2º = ω 1 /ω
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