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ÝÅÙØØÒÝÒØÖÓÙÔÓ<strong>×</strong>ÝÑÔÐØÙØÓÑÓÖÔ<strong>×</strong>Ñ<strong>×</strong>ÓK3<strong>×</strong>ÙÖ<strong>×</strong><strong>×</strong>ÙÖÓÙÔ ÔØÖºÓÒ<strong>×</strong>ØÖÙØÒØÅÓÙÐÖÓÖÑ<strong>×</strong><br />

23½℄º<br />

ØÓÖÖÓσµ<strong>×</strong>ÚÒÝ ÌÓØØÖÙÒÖ<strong>×</strong>ØÒØ<strong>×</strong>Ö<strong>×</strong>ÙÐظÓÒ<strong>×</strong>Ö<strong>×</strong>ÝÑÔÐØÙØÓÑÓÖÔ<strong>×</strong>ÑÓK3¸σ¸ÓÒØ<br />

8µºÌÒÙÑÖÓÜÔÓÒØ<strong>×</strong>¸ε(n)´ÛÔÒ<strong>×</strong>ÓÒÐÝÓÒ ÓØÅØÙÖÓÙÔ¸M<br />

ÒÔÔÒ<strong>×</strong>ØÓÑØØÒÙÑÖÓÜÔÓÒØ<strong>×</strong>ÓÖ<strong>×</strong>ÑÐÖÐÑÒØÓØÅØÙÖÓÙÔ¸<br />

ÓÖÖ¸n´Ø<strong>×</strong>ÒÓÛÒØØn ≤<br />

ÅÙØ<strong>×</strong>ÓÛØØG<strong>×</strong>ÒØÖÓÙÔÓ<strong>×</strong>ÝÑÔÐØÙØÓÑÓÖÔ<strong>×</strong>Ñ<strong>×</strong>ÓK3¸ØÒ<br />

24ÒÖÔÖ<strong>×</strong>ÒØ<strong>×</strong>ÔÖÑÙØØÓÒÖÓÙÔØÒÓÒ<strong>×</strong>Ø<br />

ε(n)<br />

24ØØÔÖ<strong>×</strong>ÖÚ<strong>×</strong>ÓÒÐÑÒØÓØ<strong>×</strong>غ<br />

M 23ºÌÅØÙÖÓÙÔM ÛØ24ÐÑÒØ<strong>×</strong>ºÌÒ¸M 23<strong>×</strong>Ø<strong>×</strong>ÙÖÓÙÔÓM (K3)ºÌÓÒÐÝÒÓÒ¹ØÖÚÐÔÖØ<strong>×</strong>ØØØÖ<strong>×</strong>ØÐ<strong>×</strong>Ø ´µGØ<strong>×</strong><strong>×</strong>ÔÖÑÙØØÓÒÓÒH∗ (K3, Z)ÒÒÑ<strong>×</strong><strong>×</strong>ÙÖÓÙÔÓM ´µGÒ<strong>×</strong><strong>×</strong>ÖÐÝ<strong>×</strong>ØÐ<strong>×</strong>ØÚÜÔÓÒØ<strong>×</strong>¸ÓÒÖ<strong>×</strong>ÒÖÓÑH0,0 H 1,1 (K3)¸H0,2 (K3)ÒH2,2 23ºÁÒ<br />

<strong>×</strong>Ô ÝÐ<strong>×</strong>Ô¾℄ºÊÐÐØØÒÝÔÖÑÙØØÓÒ´ÓÓÖÖnµÑÝÖÔÖ<strong>×</strong>ÒØÝØ<strong>×</strong>ÝÐ<br />

ÓÒÜÔÓÒØÒH1,1 24<strong>×</strong>ÐÒ ÌÑÒÓGÒØÓM 23 ⊂ M 24ÒÐ<strong>×</strong>ÓÒØÓÙ<strong>×</strong>ÒÓÛÒÔÖÓÔÖØ<strong>×</strong>ÓM ÔÖØÙÐÖ¸ØÛ<strong>×</strong><strong>×</strong>ÓÛÒÝÓÒÛÝÒÆÓÖØÓÒØØÒÝÐÑÒØÓM ÝÐ<strong>×</strong>Ô¸ρ¸<strong>×</strong><strong>×</strong>ØÓÐÒØÖÜ<strong>×</strong>Ø<strong>×</strong>ÔÓ<strong>×</strong>ØÚÒØÖM<strong>×</strong>ÙØØ<br />

ρ ≡ 1 a 1<br />

24¸ÓÒÐ<strong>×</strong>Ó<strong>×</strong>ØÓÒØÓÒ ´º¾µ<br />

2 a2 · · ·n an .<br />

) an<strong>×</strong>Ø<strong>×</strong>Ñ<strong>×</strong>ρºËÒÑ(H ´º¾µ<br />

(K3)) =<br />

ÓÐÐÓÛÒÔÖÓÙØÓη¹ÙÒØÓÒ<strong>×</strong><br />

4Ò<strong>×</strong>Ø<strong>×</strong><strong>×</strong>ØÓÚ<br />

)ÒÝØ <strong>×</strong>ÒÜÑÔиØÝÐ<strong>×</strong>Ô14 2 2 4 4<strong>×</strong>ÐÒÛØM ÓÒØÓÒºÆÓÛÚÒÐÒÝÐ<strong>×</strong>Ô¸ρ¸ÓÒ<strong>×</strong>ÖØÙÒØÓÒg )<strong>×</strong>ÒÓÖØÓÒÐÜÔÓÒÒØ<strong>×</strong>ÒØ<strong>×</strong><br />

ρ (z 1<br />

´º¾µ ÆÓØØØÛÒØÓÒØÓÒ´º¾µ<strong>×</strong><strong>×</strong>Ø<strong>×</strong>¸g ρ (z 1<br />

½<br />

( M<br />

1<br />

) a1<br />

( M<br />

2<br />

) a2<br />

· · ·(<br />

M<br />

n<br />

(K3)º<br />

24<br />

=<br />

n ∏ p|n (1 + 1) ,<br />

p<br />

∗<br />

23º<br />

∑<br />

i a i = 24 .<br />

i<br />

=<br />

ρ ↦−→ g ρ (z 1 ) ≡ η(z 1 ) a 1<br />

η(2z 1 ) a2 · · ·η(nz 1 ) an .<br />

(K3)¸H 2,0 (K3)¸

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