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From: master1729 on 28 Apr 2010 05:07
Gerry Myerson wrote :

> In article
> <29a4b1d1-8ebe-48d1-ab68-7028a0f9cfa0(a)i37g2000yqn.goog
> legroups.com>,
> Ludovicus <luiroto(a)yahoo.com> wrote:
>
> > On Apr 26, 6:54 pm, Gerry Myerson
> <ge...(a)maths.mq.edi.ai.i2u4email>
> > wrote:
> > > A modular form f has the property that if a, b,
> c, and d
> > > are integers with a d - b c = 1 then there is a
> simple relation
> > > between f( ( a z + b) / (c z + d) ) and f(z).
> > >
> > > Gerry Myerson (ge...(a)maths.mq.edi.ai) (i -> u for
> email)
> >
> > If f(z) means function of z, hitherto there is not
> problem.
> > But what simple relation is that?
>
> I'm going from memory, I'll probably get it wrong,
> you should really look it up somewhere,
> but it's something like:
>
> A modular form of weight k satisfies
> f( ( a z + b) / (c z + d) ) = |c z + d|^(- k) f(z).

and ad - bc = 1 and f(z) has period 2pi i and f is analytic in the upper half plane.

im not sure if its k or -k ...


>
> --
> Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for
> email)

regards

tommy1729
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