УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÔØÖºÅÓÙÐÖÓÖÑ<strong>×</strong><br />
ÒÖÐÐݸÓÛÚÖ¸ØØÖÑÑÓÙÐÖÙÒØÓÒ<strong>×</strong>Ù<strong>×</strong>ÓÒÐÝÓÖÑÖÓÑÓÖÔÑÓÙÐÖ<br />
Z¸ÙÒØÓÒf<strong>×</strong><strong>×</strong>ØÓÛÐÝ<br />
∗º ºÙÒØÓÒÓÒÐØØ<strong>×</strong>ÒC<strong>×</strong>Ø<strong>×</strong>ÝÒF(λL) = F(L)ÓÖÐÐÐØØ<strong>×</strong>LÒÐÐλ ∈ C<br />
Γ(1)Ò<br />
ÙÒØÓÒ<strong>×</strong><strong>×</strong>Ø<strong>×</strong>ÝÒÖØÒÖÓÛØÔÖÓÔÖØ<strong>×</strong>ºÓÖk∈<br />
ÞÖÓºÌÝÖÒÚÖÒØÙÒÖØØÓÒÓØÑÓÙÐÖÖÓÙÔºÌÔÖÓÙØÓØÛÓÛÐÝ ÖÓÑØÓÚÒØÓÒÛ<strong>×</strong>ØØØÓÒ<strong>×</strong>ØÒØÙÒØÓÒ<strong>×</strong>ÖÑÓÙÐÖÙÒØÓÒ<strong>×</strong>ÓÛØ ´º¾¼µ ÑÓÙÐÖÓÛØk¸f<strong>×</strong>ÑÖÓÑÓÖÔÙÒØÓÒÓÒH<strong>×</strong>ÙØØÓÖÐÐg∈<br />
ÖÒÓÑÓÙÐÖÙÒØÓÒ<strong>×</strong>ÓÓÛغÓÖÚÒk¸ØÓÚÕÙØÓÒ<strong>×</strong><strong>×</strong>Ñ<strong>×</strong> 2ºÌÖ ÑÓÙÐÖÙÒØÓÒ<strong>×</strong>ÓÛØ<strong>×</strong>k 1Òk 2<strong>×</strong>ÛÐÝÑÓÙÐÖÙÒØÓÒÓÛØk 1<br />
´º¾½µ<br />
+k<br />
ÑÓÙÐÖÙÒØÓÒ¸ÛÙ<strong>×</strong>ØÒØØÖÒ<strong>×</strong>ÓÖÑØÓÒÔÖÓÔÖØ<strong>×</strong>ÓØÑÖÓÑÓÖÔÙÒØÓÒ ËÒÛÒÓÛØØΓ(1)<strong>×</strong>ÒÖØÝSÒT¸ØÓÒÓÛØØÖÒ<strong>×</strong>ÓÖÑØÓÒÓÛÐÝ<br />
fÙÒÖSÒTºÑÖÓÑÓÖÔÙÒØÓÒfÓÒH<strong>×</strong><strong>×</strong>ØÓÛÐÝÑÓÙÐÖÓÛØ<br />
kØØÖÒ<strong>×</strong>ÓÖÑ<strong>×</strong>ÙÒÖSÒTÒØÓÐÐÓÛÒÛÝ<br />
k/2¸<strong>×</strong>ÒÚÖÒØÙÒÖØØÓÒÓΓ(1)º ÁÒÛÓÖ<strong>×</strong>¸ØÖÒØÐÓÖÑÓÛظf(z)(dz)<br />
´º¾¾µ<br />
ºº½ Õ¹ÜÔÒ<strong>×</strong>ÓÒ ´º¾¿µ<br />
f(− 1) = z zk f(z)<br />
′´ºº<br />
H/T¸ØØ<strong>×</strong>ØÕÙÓØÒØ<strong>×</strong>ÔÓHÑÓÙÐÓØÖÒ<strong>×</strong>ÐØÓÒÝÒØÖ<strong>×</strong>´ÝÐÒÖµºqÒÙ<strong>×</strong><br />
1ÛØØÓÖÒÖÑÓÚµºÌÙ<strong>×</strong>¸ÛÒÓÙÖÖÜÔÒf(z)<strong>×</strong><br />
Ò<strong>×</strong>ÓÑÓÖÔ<strong>×</strong>ÑØÛÒH/TÒØÔÙÒØÙÖ<strong>×</strong>ºÌÙ<strong>×</strong>¸ÑÖÓÑÓÖÔÙÒØÓÒÓÒ<br />
f(z)¸ÓÒ<strong>×</strong>ÖØ<strong>×</strong>Ô ÌÑÔz↦→ e2πizÒ<strong>×</strong>ÓÐÓÑÓÖÔÑÔÖÓÑHØÓØÔÙÒØÙÖÙÒØ<strong>×</strong>D HÛ<strong>×</strong>Ø<strong>×</strong><strong>×</strong>ØÓÒØÓÒ´º¾¿µÓÚ´ÒÚÖÒÙÒÖTµ¸ÒÙ<strong>×</strong>ÑÖÓÑÓÖÔ<br />
ÓÔÒÙÒØ<strong>×</strong>|q| <<br />
ÙÒØÓÒÓq(z) =<br />
∞ÜØÒ<strong>×</strong>ØÓ0¸Û<strong>×</strong>ÝØØf<strong>×</strong>ÑÖÓÑÓÖÔ´ÓÐÓÑÓÖÔµØÒÒØݺ<br />
−N a nq nºÌÒ¸<strong>×</strong>Òf(z+1) ∞<strong>×</strong>Ð<strong>×</strong>ÓÑÖÓÑÓÖÔØ0<strong>×</strong>ØØØÖÜ<strong>×</strong>Ø<strong>×</strong> f(z)ºÁØÑÖÓÑÓÖÔØÝ ÙÒØÓÒ¸f ∞¸ÓÒØÔÙÒØÙÖ<strong>×</strong><strong>×</strong>ÙØØf ∞ (q(z)) =<br />
´ÓÐÓÑÓÖÔØݵÓf Ò<strong>×</strong><strong>×</strong>ÖÝÒ<strong>×</strong>ÙÒØÓÒØÓÒØØf ½¾¾<br />
z ∈ H<br />
e 2πiz<strong>×</strong>f(z) = ∑ ∞<br />
f(z) = (cz + d) −k f(g · z) .<br />
f(g · z)(d(g · z)) k/2 = f(z)(dz) k/2 .<br />
f(z + 1) = f(z) .<br />
=
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