УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÔØÖºÊ<strong>×</strong>ÙÐØ<strong>×</strong>ÓØÌ<strong>×</strong><strong>×</strong><br />
ÑØÖ<strong>×</strong> ÌÐÖ<strong>×</strong>¸ÒÓØG N¸ÚØÖÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÚÒÝØÓÐÐÓÛÒPGL(2, ´º¾µ<br />
Z)<br />
Ö<strong>×</strong>ÔØØÓØØÖÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ºÁØ<strong>×</strong>ÚÒÝ℄´<strong>×</strong>Ð<strong>×</strong>Ó½¼¸½℄µ )¸ÛØ<br />
δ .<br />
ÌÏÝÐÖÓÙÔ<strong>×</strong>ÒÖØÝØØÖÐÑÒØÖÝÖØÓÒ<strong>×</strong>¸(w 1 , w 2 , w 3<br />
´º¿µ<br />
ÐØØÏÝÐÚØÓÖØØ<strong>×</strong>Ø<strong>×</strong><strong>×</strong><br />
NÐ<strong>×</strong>ÓÚ ÛÖS ÛØÐÐØÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>º<br />
3<strong>×</strong>ØÖÓÙÔÓÔÖÑÙØØÓÒ<strong>×</strong>ÓØØÖÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ºÌG ´ºµ<br />
(ρ, δ i ) = − (δ i, δ i<br />
)¸<br />
)<br />
= −1<br />
2<br />
´ÖÒصÙØÓÑÓÖÔÓÖÖØÓÒ<strong>×</strong>ØÓØÄÐÖ<strong>×</strong><strong>×</strong>ÓØÛØØÖÒØÖ ØÙÒÑÒØÐÏÝÐÑÖ<strong>×</strong>ÒØÐØØÏÝÐÚØÓÖρÓØÃÅÄ<strong>×</strong>ÙÔÖ¹<br />
NºÐÐØÐÖ<strong>×</strong>Ö<strong>×</strong><strong>×</strong> ÌÖØÒÑØÖÜA 1,II¸Ø<strong>×</strong>ØÓÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>¸δ 1 , δ 2 , δ 3¸ØÏÝÐÖÓÙÔW(A ÐÖ<strong>×</strong>G NÐ<strong>×</strong>ÓÚÑÒÖÝÖÓÓØ<strong>×</strong>ÛÓ<strong>×</strong>ÒÓÖѸÛØÖ<strong>×</strong>ÔØØÓÚÒÒÒÖÔÖÓÙØÒØ<br />
1,IIÛØÖÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÚÒÒ´º¾µºÌÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong><br />
NÓÒÓØÒÛØØÓÖÓÐÒÖÓÙÔZ 0ºÌ<strong>×</strong>ØÓÑÒÖÝÖÓÓØ<strong>×</strong> ÖØÒÑØÖÜA •ÁØÛ<strong>×</strong><strong>×</strong>ÓÛÒÒ℄ØØØÑÙÐØÔÐØ<strong>×</strong>ÓØÑÒÖÝ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÓÖ ÓÛÚÖ¸ÒÛØNºÏ<strong>×</strong>Ù<strong>×</strong><strong>×</strong>Ø<strong>×</strong>ÔÓÒØÒÜغ<br />
NÐ<strong>×</strong>ÓÓÒÓØÒÛØNºÌÖÑÙÐØÔÐØ<strong>×</strong>¸<br />
G<br />
ÖÓÓØ<strong>×</strong>Ô¸<strong>×</strong>ÒÓØÔÓ<strong>×</strong>ØÚÒظººØÒÓÖÑ(η, η) ≤<br />
ÓØÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>G NÖÖÒØÓÖÖÒØNºÌÔÖÑØÚ<br />
)ÚÒÝØÓÖÑÙÐ ØÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>G ÐعÐ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>tη<br />
ÐÒØÓØ<strong>×</strong>ÐÖ<strong>×</strong>¸ÒÒØÒÓÑÒØÓÖÒØØ<strong>×</strong>ÓØÐÖ<strong>×</strong>¸ÓÛ¹ <strong>×</strong>ÑÒØÓÒÓÚ¸ØÖØÒÑØÖܸÏÝÐÖÓÙÔ¸ÒØ<strong>×</strong>ØÓÖÐÒѹ<br />
NÖÑÒØ<strong>×</strong>ÑÓÖÐÐÚÐÙ<strong>×</strong>ÓNºÌÑÓÙÐÖÓÖÑ<strong>×</strong><br />
0ÚÑÙÐØÔÐØÝm(tη 0<br />
ÒÖÝ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÓÖØG ½<br />
( ) ( ) ( )<br />
2 1 0 −1 0 1<br />
1 = , δ 2 = , δ 3 =<br />
1 0 −1 0 1 2<br />
PGL(2, Z) = W(A 1,II ) ⋊ S 3 ,<br />
1 − ∑ t∈N<br />
m(tη 0 ) q n =<br />
√<br />
gρ (τ)<br />
η(τ) 3<br />
1,II
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