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Ó<strong>×</strong>ÐÐØÓÖ<strong>×</strong>ÖÝÒÑÓÑÒØÙÑ−l/NºÌ<strong>×</strong>Ú<strong>×</strong> ÔØÖ¾ºÓÙÒØÒÝÓÒ<strong>×</strong>ÒËØÖÒÌÓÖÝ<br />

ÛÖØØÓÖÓ16ÓÑ<strong>×</strong>ÖÓÑØÖÑÓÒÞÖÓÑÓ<strong>×</strong>ºÌÓÒ<strong>×</strong>ØÒØCÖÔÖ<strong>×</strong>ÒØ<strong>×</strong>Ø ´¾ºµ<br />

0/NÕÙÒØÙÑÒÙÑÖÓØÚÙÙÑÓØÃÐÙÞ¹ÃÐÒÑÓÒÓÔÓÐÛÒÐÐØÓ<strong>×</strong>ÐÐØÓÖ<strong>×</strong><br />

(1 − e 2πıeρl ) −n l<br />

,<br />

−l ′<br />

ÖÒØÖÖÓÙÒ<strong>×</strong>ØØÒ<strong>×</strong>ÕÙÐØÓC<br />

r,sÝ<br />

´¾ºµ<br />

=<br />

ÛÖ˜α<strong>×</strong>ÚÒÒØÖÑ<strong>×</strong>ÓQ ÈÙØØÒØÐÐØÓØÖ¸ÛØ ´¾ºµ<br />

(−1))´¾º¼µ<br />

(1 − e 2πıs/N ) 2.<br />

¾ºº¾ ÓÙÒØÒËØØ<strong>×</strong><strong>×</strong><strong>×</strong>ÓØÏØØÊÐØÚÅÓØÓÒÓØ 1¹5ËÝ<strong>×</strong>ØÑ<br />

1<br />

ØÔÐÒÓØ5¹ÖÒ¸Û<strong>×</strong>ØÖØÝÓÒ<strong>×</strong>ÖÒ<strong>×</strong>ÒÐ1¹ÖÒÑÓÚÒÒ<strong>×</strong>5¹<br />

D1¸ÛÓÙÒØ<strong>×</strong>Ø<strong>×</strong>ØØ<strong>×</strong><strong>×</strong><strong>×</strong>ÓØÛØØÑÓØÓÒÓØ1¹ÖÒÒ<br />

ÔÖ<strong>×</strong>ÒÓØÃÐÙÞ¹ÃÐÒÑÓÒÓÔÓиØØÛÓ¹ÑÒ<strong>×</strong>ÓÒÐØÓÖÝ<strong>×</strong>ÖÒØ<strong>×</strong><strong>×</strong>Ý<strong>×</strong>ØÑ ÖÒºÏÒÐÝÞØÛÓÖйÚÓÐÙÑØÓÖÝÓ<strong>×</strong>ÒÐD1¹ÖÒÒ<strong>×</strong>D5¹ÖÒºÁÒØ ÛÓÙÔÐÒÐÑØØÝÒÑ<strong>×</strong>ÓØ1¹ÖÒÒ<strong>×</strong>5¹ÖÒ<strong>×</strong>Ò<strong>×</strong>Ò<strong>×</strong>ØÚØÓØ<br />

ÌÓÓÑÔÙØd 4)<strong>×</strong>ÙÔÖ<strong>×</strong>ÝÑÑØÖݺÓÒ<strong>×</strong>Ö1¹ÖÒÛÖÔÔÒÐÓÒØÖØÓÒÒÛ<br />

N¸ØÒσÒ<strong>×</strong>Ý2πwÛÒÛØÖÚÖ<strong>×</strong> <strong>×</strong>(4,<br />

S 1 /Z N<strong>×</strong>ÔÖÓ2πºÄØσÒÓØØÓÓÖÒØÐÓÒØÐÒØÓØ1¹ÖÒÒw ØÛÒÒÒÙÑÖÓØ1¹ÖÒÐÓÒS1 /Z<br />

ØÛÓÐÐÒØÓØ<strong>×</strong>ØÖÒ¸ÛÐØÔÝ<strong>×</strong>ÐÓÓÖÒØÓØ1¹ÖÒ<strong>×</strong>Ø<strong>×</strong>Ý2πr ÐÓÒS1ÛÖrÒwÖÖÐØ<strong>×</strong>r ½<br />

=<br />

g(˜ρ) ≡ ∑ −l ′ 0<br />

∑<br />

∞∏<br />

d KK (l 0)e ′ 2πıeρl′ 0 = 16e<br />

2πıNC eρ<br />

l ′ 0<br />

−˜α/N,<br />

˜α = 1<br />

24N Q 0,0 − 1<br />

N−1<br />

∑<br />

2N<br />

d KK (−l ′ 0 )e2πıeρl′ 0 = 16e<br />

−2πıeαeρ<br />

s=1<br />

Q 0,s<br />

l=1<br />

e 2πıs/N<br />

∞∏<br />

(1 − e 2πıeρl ) − P N−1<br />

l=1<br />

w modN .‘ ´¾º½µ<br />

s=0 e2πıls/N (c (0,s)<br />

0 (0)+c (0,s)

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