ÜBER DIE LINEARE TRANSFORMATION D. THETAFUNCTIONEN. 69 



V. 



a Q = 1 , % = ; b = 1 , \ = 1 (mod 2) 

 9x 1 = 9i + h > hi = h ( mod 2 ) 



a x (a -\-ait)v'-rti C — -j (a b — 2 ö ) tz i , 



e ^0 0> *) = n/ r- = • e #3 K * ) 



ai(Oo + ai*)»' 2 Äi C ' _. , , ,s 



e ^1 ('•'; V = , , — • X (v , T ) 



a n -+- a, x 



a 1 (a, + a 1 t)v' n -7ti c — t^i 6 ! - 2 *i + 2 ) ni „ / , , N 



e 2 (*>, *) = — • e 2 (ü , t ) 



ya -\- cl x t 



e #3 ( V; T ) == 



"|/a -\- a r r 



— T(aol>o + 2a b 1 + a 1 b 1 — 2(a + a l +b + b 1 — l))7ti , 



X e 4 v y O (t> , T ) 



Im einfachsten Fall 



a = 1 ? « x = , & = — 1 ; &J == 1 

 ist wegen a x = die Formel (16) anzuwenden. Es wird 

 x = % — 1 ; v' = v 2 t = t'4~1? ü = « 



X (t>, t) = e 4 X (V, t') 

 #2 (v,t) = e i 1 & 2 (v',t) 



#3 C y > T ) == #0 0'; O 



VI. 



a = , a x = 1 , & = 1 , & x = 1 (mod 2) 

 ^x = 9a + *a , hi = 9i (mod 2) 



ai(aoH-«i*)o' 2 Ä*' , N , C — 4-K&0— 26 )äi , , ,. 



e fr fo, *) = . — ;— = • e 4 -^(^r) 



ya -f- a t x 



e äi («, r) = -7== -öii*,*) 



ya -\- CI-L x 



a 1 {a + a ] t)v' i 7ti c — t(Mi — 2&! + 2)«; , 



e 2 ( V; T ) = = • e 4 3 (ü ; r ) 



y« 4- Oi t 



