On the multipliers of Dedekind modular function

Joseph Lehner
1968 Journal of Research of the National Bureau of Standards Section B Mathematical Sciences  
Th e Ded e kind modul ar fun c tio n is d efined by 1)(r) =e"iT/12 IT (I -e 2 " i"'T), 1m r > O, and satisfie s I the tran sformation equati on (cr+dt ' / 2 1) (A r) = v(A)1)(r) for ever y Ae l', th e modular group , where v(A) is a compli ca te d 24t h root of unit y d epe ndin g on A . Le t C be th e se t of all Aer for which v(A) = 1. Then C is not a g ro up , but the re are group s th at are s ubsets of G, eg., {52'}, where 5 = (~ ~). Main Theo rem. Eve ry s ubgro up of r th at is a s ub se
more » ... th at is a s ub se t of G is cyc lic. Moreover Cc 1" , th e co mmutator s ub gro up of r.
doi:10.6028/jres.072b.025 fatcat:zmyllemhizeoddgqhduvhpmfmy