УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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2ζ(2k)ºÌ<strong>×</strong><strong>×</strong>ÐÐØÒÓÖÑÐÞ<strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong> ÔØÖºÅÓÙÐÖÓÖÑ<strong>×</strong><br />
´º½µ<br />
Ò<strong>×</strong>ØÓØÛÓÐÑÓÙÐÖÖÓÙÔºÌ<strong>×</strong>Ú<strong>×</strong><strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>ØÐÚÐNºÐÓÛÛÚ <strong>×</strong>ÓÑÜÔÐØÜÔÒ<strong>×</strong>ÓÒ<strong>×</strong>Ó<strong>×</strong>ÓÑÓØ<strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>ØÚÖÓÙ<strong>×</strong>ÐÚÐ<strong>×</strong>º <strong>×</strong>ÓÖ¸ÛÒÐ<strong>×</strong>ÓÓÒ<strong>×</strong>Ö<strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>ÛØÖ<strong>×</strong>ÔØØÓ<strong>×</strong>ÙÖÓÙÔΓ(N)ÓΓ(1)¸<br />
E 2k (z) = G 2k(z)<br />
2ζ(2k) .<br />
<strong>×</strong>ÑÓÙÐÖÓÖÑØ<strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>ÛÐÐÑØq¹ÜÔÒ<strong>×</strong>ÓÒ<strong>×</strong>ÓÖÑÐÔÓÛÖ<strong>×</strong>Ö<strong>×</strong>Ò ºº¾ ÓÙÖÖÜÔÒ<strong>×</strong>ÓÒ<strong>×</strong>Ó<strong>×</strong>Ò<strong>×</strong>ØÒËÖ<strong>×</strong><br />
<strong>×</strong>ÑÙÒØÓÒ<strong>×</strong>Ò<strong>×</strong>Ø<strong>×</strong>ÙÑÓØr¹ØÔÓÛÖ<strong>×</strong>ÓØÔÓ<strong>×</strong>ØÚÚ<strong>×</strong>ÓÖ<strong>×</strong>Ónººº ÒØÓÒºº½ËÑÙÒØÓÒÓÖÒÒØÖr≥0ÒÒÝÔÓ<strong>×</strong>ØÚÒØÖn¸Ø<br />
nÒØ<strong>×</strong>ÑÙÒØÓÒÛÛÒÐÓÛº ØÖÑ<strong>×</strong>Óq(z) = e 2πiτºÀÖÛÚØÓÙÖÖÜÔÒ<strong>×</strong>ÓÒÓØ<strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>G ØÖÑ<strong>×</strong>ÓÖÒÓÙÐÐÒÙÑÖ<strong>×</strong>B ´º¾µ<br />
ØÓÐÐÓÛÒÕÙÐØÝÓÓÖÑÐÔÓÛÖ<strong>×</strong>Ö<strong>×</strong><br />
n¸ÖÒÝ ÏÐ<strong>×</strong>Ó<strong>×</strong>Øσ 0 (n) = d(n)ÓÖØÒÙÑÖÓÔÓ<strong>×</strong>ØÚÚ<strong>×</strong>ÓÖ<strong>×</strong>ÓnÒσ(n) ÒØÓÒºº¾ÖÒÓÙÐÐÆÙÑÖ<strong>×</strong>ÓÖn ≠ 0ØÖÒÓÙÐÐÒÙÑÖ<strong>×</strong>¸B Í<strong>×</strong>ÒØÓÚØÛÓÒØÓÒ<strong>×</strong>¸ÛÒÛÖØØÓÙÖÖÜÔÒ<strong>×</strong>ÓÒÓØÒÓÖÑÐÞ<strong>×</strong>Ò¹ ´º¿µ<br />
2k<strong>×</strong>¿<br />
n! . ´ºµ <strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>E<br />
ÓÙØÖÒØÙ<strong>×</strong>Ô<strong>×</strong><strong>×</strong><strong>×</strong>Ù<strong>×</strong><strong>×</strong>ÒÔÔÒܺÐÓÛ¸<strong>×</strong>ÒÜÑÔиÛÚØÓÙÖÖ ÓÖ<strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>ÓÖÐÚиÛÚØÓÓÑÔÙØØÖÜÔÐØÓÖÑÙ<strong>×</strong>ÒÚÖÓÙ<strong>×</strong><br />
2k<strong>×</strong>º<strong>×</strong>Ù<strong>×</strong><strong>×</strong>ÓÒÓ<strong>×</strong>Ò<strong>×</strong>ØÒ<strong>×</strong>Ö<strong>×</strong>ØÐÚÐNÒØÖÜÔÒ<strong>×</strong>ÓÒ<strong>×</strong><br />
E<br />
ÖÐØÓÒ<strong>×</strong>ØÛÒØE 2<strong>×</strong>ÒÐÓÛ<strong>×</strong>ÒÓØÑÓÙÐÖÓÖÑ<strong>×</strong>ÓÛØØÛÓÙØÓÓÒÚÖÒºÐÓ<strong>×</strong>ÐÝÖÐØÒÓÒ¹<br />
)<strong>×</strong>ÛØØÛÓ´ËÔÔÒܵ ½¾<br />
¿E<br />
ÓÐÓÑÓÖÔÓÖÑE 2 ∗ = ( E 2 − 3<br />
ÁÑz<br />
k<br />
σ r (n) = ∑<br />
d r .<br />
1≤d|n<br />
= σ 1 (n)º<br />
∞<br />
x<br />
e x − 1 = ∑ x n<br />
B n<br />
2k = 1 − 4k<br />
B 2k<br />
n=0<br />
∞<br />
∑<br />
n=1<br />
σ 2k−1 (n)q n .<br />
(z)Ò
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