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ÔØÖºÓÒ<strong>×</strong>ØÖÙØÒØÅÓÙÐÖÓÖÑ<strong>×</strong><br />

ØÑ<strong>×</strong>ÐÚ<strong>×</strong>ÖÐ<strong>×</strong>ÓÑÓÙÐÖÓÖÑ<strong>×</strong>¸ÒØÓÖÑÓÒÒÒØ<strong>×</strong>ÙÑÒÒÒÒØÔÖÓÙØ<br />

(Z)Ö<strong>×</strong>ÔØÚÐݸÒÓÖÖØÓÙÒÖ<strong>×</strong>ØÒØÐÖ<strong>×</strong>ØÖÙØÙÖ (Z)¸Û<br />

(Z)ÒΦ ÏÛÐÐÐ<strong>×</strong>ÓÒØÓ<strong>×</strong>ØÙÝØ<strong>×</strong>ÕÙÖÖÓÓØ<strong>×</strong>³ÓØÑÓÙÐÖÓÖÑ<strong>×</strong>˜Φk<br />

ÒÜØÔØÖ¸ÒÒ¸ØÓÒØÖÔÖØØÑ<strong>×</strong>Ø<strong>×</strong>ÙÑÒÔÖÓÙØ<strong>×</strong>ÓÒÓÑÒØÓÖ<br />

k<br />

ÒÓؘ∆k/2 (Z)Ò∆ k/2<br />

(Z)ºÌ<strong>×</strong>ÑÓÙÐÖ ÙÒÖÐÝÒØÒÖÝÓØ1<br />

ÒØØݸÓÒ<strong>×</strong>ØÓÔÖÓÚØÖÑÓÙÐÖÔÖÓÔÖØ<strong>×</strong>ÛÛÛÐÐ<strong>×</strong>ÓÛÒØ<strong>×</strong>ÔØÖº ÓÖÑ<strong>×</strong>Ö<strong>×</strong><strong>×</strong>ØÒÓÑÒØÓÖÓÖÑÙÐÓÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong><strong>×</strong>ÛÛÐÐ<strong>×</strong>ØÙÝÒØ<br />

(Z)Ò∆ 4¹ÈË<strong>×</strong>ØØ<strong>×</strong>ºÏÛÐÐÓØÒ˜∆k/2 k/2<br />

(Z)ÒΦ ÐÓÒØÐÒ<strong>×</strong>ÓØÓÒ<strong>×</strong>ØÖÙØÓÒÓØÑÓÙÐÖÓÖÑ<strong>×</strong>˜Φk<br />

º¾º½ º¾ ÅÓÙÐÖÓÖÑ<strong>×</strong>ÚØØÚÐØ ØÚÐØÓÂÓÓÖÑ<strong>×</strong>ÛØÒØÖÒÜ<br />

k<br />

ÂÓÓÖÑ<strong>×</strong>ÓÒ<strong>×</strong>ØÖÙØ<strong>×</strong>ÑÒØÓÒÒØÔÖÚÓÙ<strong>×</strong><strong>×</strong>ØÓÒºÚÒÂÓÓÖÑÓ<br />

(Z)ÖÓÑØÛ<br />

ÜÔÐØÓÖÑÙÐ℄Ù<strong>×</strong>ÒØÓÒØ<strong>×</strong>ÓØÓÙÖÖÜÔÒ<strong>×</strong>ÓÒÓØÂÓÓÖѺÌ<strong>×</strong> ÔÖÓÙÖ<strong>×</strong>ÒÓÛÒ<strong>×</strong>ØÖØÑØÓÖØÚÐØÓØÂÓÓÖѺÁØ<strong>×</strong>ÒÓÛÒØØ ÛØkÒÒÜ1¸ÅÓÒ<strong>×</strong>ØÖÙØËÐÑÓÙÐÖÓÖÑÓÛØkÐÒØÓÒ<br />

(Z)ÒΦ ÆÓÛÛÓÑØÓØÓÒ<strong>×</strong>ØÖÙØÓÒÓØÑÓÙÐÖÓÖÑ<strong>×</strong>˜Φk<br />

(Z)¸<strong>×</strong>ÒÖØÝØÂÓÓÖÑ<br />

k<br />

ÅÓÖÒÖÐÐݸÓÒ<strong>×</strong>ÖÛÂÓÓÖÑÓÛØk¸ÒÜ1ÒÐÚÐN<strong>×</strong> ´ºµ<br />

ØÖÒÓËÐÑÓÙÐÖÓÖÑ<strong>×</strong><strong>×</strong>ÒÖØÝÓÙÖÑÓÙÐÖÓÖÑ<strong>×</strong>ÛØÛØ<strong>×</strong>4¸6¸10 Ò12ºÓÖÒ<strong>×</strong>ØÒ¸ØÛØ10ÑÓÙÐÖÓÖÑ¸Φ 10<br />

ÓÛØ10ÒÒÜ1<br />

´ºµ<br />

ØÖºÏÛÐÐÖÖØÓØÛÂÓÓÖÑ<strong>×</strong>ØØÚ<strong>×</strong>ºÌÅÓÒ<strong>×</strong>ØÖÙØÓÒ ´ÒÖÐÞØÓÖÐÚÐ<strong>×</strong>ÒÑÓÙÐÖÓÖÑ<strong>×</strong>ÛØÖØÖÝÂØÖÒËÒ¾℄µÐ<strong>×</strong><br />

2)ØÐÚÐNÔÓ<strong>×</strong><strong>×</strong>ÐÝÛØÖ¹ ÛÖg ρ (z 1<br />

l)¸<br />

)<strong>×</strong>ÒÙ<strong>×</strong>¹ÓÒÑÓÙÐÖÓÖÑÓÛØ(k<br />

´ºµ<br />

ØÓØÓÐÐÓÛÒÓÖÑÙÐÓÖÛØkÑÓÙÐÖÓÖÑÚÒÝØÓÙÖÖÓÒØ<strong>×</strong>¸a(n, ÓØØÚ<strong>×</strong>Φ k (Z) ≡<br />

χ(d) d k−1 a ( )<br />

nm, l d 2 d q n r l s m ,<br />

½¾<br />

φ 10,1 (z 1 , z 2 ) = θ 1 (z 1 , z 2 ) 2 η(z 1 ) 18 .<br />

φ k,1 (z 1 , z 2 ) = ϑ 1(z 1 , z 2 ) 2<br />

g<br />

η(z 1 ) 6 ρ (z 1 ) = ∑ a(n, l) q n r l ,<br />

n,l<br />

+<br />

∑<br />

∑<br />

(Z)¸<br />

(n,l,m)>0<br />

d|(n,l,m)

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