УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÛÖ ÔØÖºÓÒ<strong>×</strong>ØÖÙØÒØÅÓÙÐÖÓÖÑ<strong>×</strong><br />
Òχ(d)<strong>×</strong>ÖÐÖÐØÖØÖ℄ÑÓÙÐÓNºÌÛØkÒØÖØÖχÖ<br />
)ºÏÒχ(d)<strong>×</strong>ØÖÚиºº¸<br />
(n, l, m) > 0ÑÔÐ<strong>×</strong>n, ØÖÑÒÝØÑÓÙÐÖÓÖÑg ÛÓØÒÐÚÐNËÐÑÓÙÐÖÓÖѺÏÒØÂÓÓÖÑ<strong>×</strong>ÓÒÛØÖØÖ¸ÓÒ ´ºµ<br />
ρ (z<br />
<strong>×</strong><strong>×</strong>ØÔÔÖÒÓÒÓÒ¹ØÖÚÐÖÐØÖØÖÒØËÐÑÓÙÐÖÓÖÑÓØÒ ÖÓÑØØÚÐØ<strong>×</strong>ÓÒÛØÖØÖº<br />
1<br />
1ÓØÖÛ<strong>×</strong>,<br />
º¾º¾ ÒØÖÐÒܺÏÛÐÐÒÓÛ<strong>×</strong>ØÙÝÜÑÔÐ<strong>×</strong>ÛØйÒØÖÐÒܸ<strong>×</strong>ØÝÔÔÖÒØ ÏÚÙ<strong>×</strong>ØÓÒ<strong>×</strong>ÖÑÓÙÐÖÓÖÑ<strong>×</strong>ÓØÒÖÓÑØØÚÐØÓÂÓÓÖÑ<strong>×</strong>ÛØ ØÚÐØÓÂÓÓÖÑ<strong>×</strong>ÛØйÒØÖÒÜ<br />
NÒ˜GNºØØÛÓÒ<strong>×</strong>ÖÒ<br />
ÒÜ1/2ÛØÖØÖºÌ<strong>×</strong>ÂÓÓÖÑÔÔÖ<strong>×</strong><strong>×</strong>ØÒÓÑÒØÓÖÓÖÑÙÐÓØÒ ØÒÜØÔØÖºÌ<strong>×</strong>ÑÔÐ<strong>×</strong>ØÜÑÔÐÓÑÓÙÐÖÓÖÑÛØйÒØÖÐÒÜ<strong>×</strong>ÚÒ<br />
)ºÁØ<strong>×</strong>ÓÐÓÑÓÖÔÂÓÓÖÑÓÛØ1/2Ò ÒÓÑÒØÓÖÓÖÑÙÐÓÖØØÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>G ÝØÂÓØØÙÒØÓÒ¸ϑ<br />
ÒÜ<strong>×</strong>ÓØÓÖÑ )ºÌÓÙÖÖÜÔÒ<strong>×</strong>ÓÒÓ<strong>×</strong>ÙÂÓÓÖÑÛØйÒØÖÐ<br />
1 (z 1 , z 2<br />
(N)ÓÛØk/2Ò Ã¹ÅÓÓÝÐָ (1)<br />
(Z)Ò∆ 1ºÙÖØÖ¸ÛÛÐÐ<strong>×</strong>ØØØÑÓÙÐÖÓÖÑ<strong>×</strong>˜∆k/2 ÒÐ<strong>×</strong>ÓÓØÒ<strong>×</strong>ØØÚÐØÓÂÓÙ<strong>×</strong>ÔÓÖÑÓΓ 1<br />
ÒÜ1/2 ψ k/2,1/2 (z 1 , z 2<br />
´ºµ<br />
ÒÝØØÚÐظ<strong>×</strong>ÔÔÒÜ℄<br />
ψ<br />
exp(2πiz 3 )ºÌÑÓÙÐÖÓÖÑ∆ ÛÖχ(d)<strong>×</strong>ØÖØÖ<strong>×</strong><strong>×</strong>ÓØÛØØØÚ<strong>×</strong>º ´º½¼µ<br />
, l d q n/2 r l/2 s m/2 , 2 ½¿<br />
m ∈ Z + , l ∈ ZÒ(4nm − l 2 ) > 0<br />
χ(d) =<br />
{<br />
k/2,1/2 (z 1 , z 2 ) =<br />
0(d, N) ≠ 1<br />
∑<br />
n,l≡1ÑÓ2<br />
ÛØq=exp(2πiz 1 )Òr=exp(2πiz 2 )Òs =<br />
∆ k/2 (Z) ≡<br />
∑<br />
(n,l,m)>0<br />
∑<br />
d|(n,l,m)<br />
g(n, l) q n/2 r l/2 ,<br />
χ(d) d k−2<br />
2 g ( nm<br />
k/2<br />
(Z)<br />
(Z)<strong>×</strong>
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