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ÔØÖºÓÒÐÙ<strong>×</strong>ÓÒÒÙØÙÖÖØÓÒ<strong>×</strong><br />
ÑØÑØÐ<strong>×</strong>ØÖÙØÙÖÐÝ<strong>×</strong>ÝÑÑØÖÝ<strong>×</strong>ÔºÇÙÖÙÐØÑØÑ<strong>×</strong>ØÓÙÒÖ<strong>×</strong>ØÒØ ½¾¼¸½¾½℄º<strong>×</strong>ÑÒØÓÒÓÖ¸ØÖÓ<strong>×</strong>ÙÔÖ<strong>×</strong>ÝÑÑØÖÝÑ<strong>×</strong>ÐÐØÙØÙÐ<br />
2<strong>×</strong>ÙÔÖ<strong>×</strong>ÝÑÑØÖݽ½¸<br />
ÑÓÐ<strong>×</strong><strong>×</strong>ÓÓÛÝØÓÒÐÐÝÖÙØÒØÓØÒÖÐ<strong>×</strong>º ÑÖÓ<strong>×</strong>ÓÔ<strong>×</strong>ÖÔØÓÒÓÒÖÐÐÓÐ<strong>×</strong>ºÓÖØ<strong>×</strong>Ø<strong>×</strong>Ò<strong>×</strong><strong>×</strong>ÖÝØÓÙÒÖ<strong>×</strong>ØÒØ<br />
ÇÒÒÐ<strong>×</strong>ÓÖÖÝÓÙØ<strong>×</strong>ÑÐÖÔÖÓÖÑÑÓÖÑÓÐ<strong>×</strong>ÛØN =<br />
ÓÚ<strong>×</strong>ÛÒØÖÓ<strong>×</strong>ÝÑÑØÖÝÓØ<strong>×</strong>Ý<strong>×</strong>ØÑ<strong>×</strong>ÖÙºËØÖØÒÛØN =<br />
2<br />
½
ÔØÖºÓÒÐÙ<strong>×</strong>ÓÒÒÙØÙÖÖØÓÒ<strong>×</strong> ÑØÑØÐ<strong>×</strong>ØÖÙØÙÖÐÝ<strong>×</strong>ÝÑÑØÖÝ<strong>×</strong>ÔºÇÙÖÙÐØÑØÑ<strong>×</strong>ØÓÙÒÖ<strong>×</strong>ØÒØ ½¾¼¸½¾½℄º<strong>×</strong>ÑÒØÓÒÓÖ¸ØÖÓ<strong>×</strong>ÙÔÖ<strong>×</strong>ÝÑÑØÖÝÑ<strong>×</strong>ÐÐØÙØÙÐ 2<strong>×</strong>ÙÔÖ<strong>×</strong>ÝÑÑØÖݽ½¸ ÑÓÐ<strong>×</strong><strong>×</strong>ÓÓÛÝØÓÒÐÐÝÖÙØÒØÓØÒÖÐ<strong>×</strong>º ÑÖÓ<strong>×</strong>ÓÔ<strong>×</strong>ÖÔØÓÒÓÒÖÐÐÓÐ<strong>×</strong>ºÓÖØ<strong>×</strong>Ø<strong>×</strong>Ò<strong>×</strong><strong>×</strong>ÖÝØÓÙÒÖ<strong>×</strong>ØÒØ ÇÒÒÐ<strong>×</strong>ÓÖÖÝÓÙØ<strong>×</strong>ÑÐÖÔÖÓÖÑÑÓÖÑÓÐ<strong>×</strong>ÛØN = ÓÚ<strong>×</strong>ÛÒØÖÓ<strong>×</strong>ÝÑÑØÖÝÓØ<strong>×</strong>Ý<strong>×</strong>ØÑ<strong>×</strong>ÖÙºËØÖØÒÛØN = 2 ½
A ÌØÙÒØÓÒ<strong>×</strong> ÌÒÙ<strong>×</strong>¹ÓÒØØÙÒØÓÒ<strong>×</strong>ÖÒÝ º½ ÒÙ<strong>×</strong>¹ÓÒØØÙÒØÓÒ<strong>×</strong> ´º½µ z)ÙÒÖÑÓÙÐÖØÖÒ<strong>×</strong>ÓÖÑØÓÒ<strong>×</strong><strong>×</strong>ÚÒÝ )º )¸ ÛÖa.b ∈ (0, 1) mod 0] 2ºÇÒ<strong>×</strong>ϑ (z1 , z 2 ] (z1 , z 2 1] )Òϑ (z1 , z 2 ÌØÖÒ<strong>×</strong>ÓÖÑØÓÒ<strong>×</strong>Óϑ 1 ´º¾µ (τ, ÌÒØÙÒØÓÒη(τ)<strong>×</strong>ÒÝ ÌØÖÒ<strong>×</strong>ÓÖÑØÓÒÓØÒØÙÒØÓÒÙÒÖØÑÓÙÐÖÖÓÙÔ<strong>×</strong>ÚÒÝ´º¿µ (1 − q n ) . ϑ 3 (z 1 , z 2 ) ≡ θ [ 0 0 [ a θ (z 1 , z 2 ) = b] ∑ q 1 2 (l+ a 2 )2 r (l+ a 2 ) e iπlb , l∈Z 1 4 (z 1 , z 2 ) ≡ θ [ 0 ÛØq= exp(2πiτ)Òr=exp(2πiz)º (z 1 , z 2 ) ≡ θ [ ] 1 (z1 , z 2 )¸ϑ 2 (z 1 , z 2 ) ≡ θ [ 1 T : ϑ 1 (τ + 1, z) = e iπ/4 ϑ 1 (τ, z) , S : ϑ 1 (−1/τ, −z/τ) = − 1 q 1/2 r eπiz2 /τ ϑ 1 (τ, z) , η(τ) = e 2πiτ/24 ∞ ∏ n=1 1 T : η(τ + 1) = e πi/12 η(τ) , S : η(−1/τ) = e −πi/4 (τ) 1/2 η(τ) . ´ºµ ½
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