УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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<strong>×</strong>ÓÛ<strong>×</strong>ØØfÑÔ<strong>×</strong>˜CØÓ˜CºÌÙ<strong>×</strong>¸ØÒÚÖ<strong>×</strong>Óf<strong>×</strong>Ð<strong>×</strong>ÓÅÙ<strong>×</strong>ØÖÒ<strong>×</strong>ÓÖÑØÓÒÒØ ÔØÖºÅÓÙÐÖÓÖÑ<strong>×</strong><br />
ÒÚÖ<strong>×</strong>ÑØÖÜ ´º½¾µ<br />
1ÓÖÑ<strong>×</strong>ÖÓÙÔºÌ<strong>×</strong><strong>×</strong>ÒÓ<strong>×</strong>ÙÖÔÖ<strong>×</strong><strong>×</strong>ØÑØÖ<strong>×</strong>A<strong>×</strong>ÒÓÚÖÙ<strong>×</strong>ØØ<strong>×</strong>ÙÖÓÙÔ<br />
)<br />
A<br />
ÑÓÙÐÖÖÓÙÔº 1ºÁÒ<strong>×</strong>ØÙÝÒÑÓÙÐÖÓÖÑ<strong>×</strong>Û<strong>×</strong>ØÙÝÒÑÔÓÖØÒØ<strong>×</strong>ÙÖÓÙÔ<br />
dÖØÒØÓÒØÖ<strong>×</strong>ºÁØ<strong>×</strong>ÐÐØ<br />
ÓÖÖ<strong>×</strong>ÔÓÒ<strong>×</strong>ØÓf −1 (z)ºÌÙ<strong>×</strong>¸Û<strong>×</strong>ØØØ<strong>×</strong>ØÓÐÐÅÙ<strong>×</strong>ØÖÒ<strong>×</strong>ÓÖÑØÓÒ<strong>×</strong>ÛØad−bc<br />
º¿<br />
ÓSL(2,<br />
ÌÅÓÙÐÖÖÓÙÔÒÙÒÑÒØÐÓÑÒ<br />
Z)ÛØØA ÓØ<strong>×</strong>ÖÓÙÔ¸ÛÖÐÐØÓÒØ<strong>×</strong>a, b, c,<br />
Ì<strong>×</strong>ØÓÐÐÅÙ<strong>×</strong>ØÖÒ<strong>×</strong>ÓÖÑØÓÒ<strong>×</strong>ÓØÓÖÑ ´º½¿µ<br />
<strong>×</strong>ÐÐØÑÓÙÐÖÖÓÙÔ¸ÒÓØΓ(1)´ÌÖÙÑÒØ1ÓÑ<strong>×</strong>ÐÖÐØÖ¸ÛÒÛ <strong>×</strong>Ù<strong>×</strong><strong>×</strong>ÓÒÖÙÒØ<strong>×</strong>ÙÖÓÙÔ<strong>×</strong>µºÖÓÑØ<strong>×</strong>ÒØÓÒ<strong>×</strong>ÛÒ<strong>×</strong>ØØØ<strong>×</strong><strong>×</strong>Ù<strong>×</strong>ØØÖÓÙÔ<br />
1¸ÒÑØÖÜAÒØÛØØ<strong>×</strong>ÒØÚ¸−A¸<br />
z ′ = az + b<br />
cz + d ,<br />
ÛØa,<br />
ÜÑÔÐÓÑÓÙÐ<strong>×</strong>Ôº<br />
HÖÑÓÙÐÓÖØ<strong>×</strong>ÓÑÓÖÔ<strong>×</strong>ÑÐ<strong>×</strong><strong>×</strong><strong>×</strong>ÓÐÐÔØÙÖÚ<strong>×</strong>ÓÚÖCºÁØ<strong>×</strong>Ø<strong>×</strong>ÑÔÐ<strong>×</strong>Ø<br />
Z)¾ºÌÖÓÙÔØ<strong>×</strong>Ø<strong>×</strong>ÒÑÖÓÑØØØØØÔÓÒØ<strong>×</strong>ÓØÕÙÓØÒØ<strong>×</strong>Ô<br />
b, c, dÒØÖ<strong>×</strong>¸Òad bc =<br />
Z)ÓÒ˜C<strong>×</strong>ÓÐÐÓÛ<strong>×</strong>ºÄØ<br />
PSL(2, ˜CÒÝÔÓÒØÒ˜Cº<br />
Γ(1) \<br />
ÄØHØÙÔÔÖÐÔÐÒºÏÙÒÖ<strong>×</strong>ØÒØØÓÒÓSL(2,<br />
∈ SL(2, Z)ÒÝÐÑÒØÓSL(2, Z)ÒÐØz ∈<br />
ÏÖÖÔÖ<strong>×</strong>ÒØÒØØÖÒ<strong>×</strong>ÓÖÑØÓÒÝØÑØÖÜ<strong>×</strong><strong>×</strong>ÓØÛØغÏÒÓØØ ´º½µ ÌÒ¸ØØÓÒÓgÓÒz<strong>×</strong>ÚÒÝg<br />
)¸ÖÓÑØ<strong>×</strong>ÒØØ<strong>×</strong>ØÖÚÐÐÝÓÒHº Z)ØÑÓÙÐÖÖÓÙÔºÏÖÑÓÒÓÙØØÒØÖÓØÖÓÙÔ¸<br />
·<br />
¾ËÓÑÓÓ<strong>×</strong>ÐÐØÖÓÙÔSL(2,<br />
½½<br />
g ≡<br />
(<br />
(<br />
1 0<br />
±<br />
0 1<br />
(<br />
−1 d −b<br />
=<br />
−c a<br />
=<br />
=<br />
a b<br />
c d<br />
−<br />
)<br />
z ≡ az + b<br />
cz + d .
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