NetNews Usenet Archive 1992 #20/NN_1992_20.iso/spool/sci/math/11120

Text File | 1992-09-08 | 1.4 KB | 37 lines

Newsgroups: sci.math
Path: sparky!uunet!gatech!darwin.sura.net!Sirius.dfn.de!th-ilmenau.RZ.TH-Ilmenau.DE!hpux.rz.uni-jena.de!mwj
From: [e-mail] (Johannes Waldmann)
Subject: Re: SL(2,Z) fundamental domain
Message-ID: <[e-mail]>
Organization: University Jena, Germany
References: <[e-mail]>
Date: Tue, 08 Sep 1992 15:02:18 GMT
Lines: 26

In article <[e-mail]> [e-mail] (Johannes Waldmann) writes:
>The classical picture of the standard fundamental domain for SL(2,Z)
>and its images in the upper half plane consists of (lines and)
>semicircles with rational midpoints and radii. Is there an explicit
>formula that tells what centre points and radii do really occur?

That's actually me discussing with myself, but I'll try this one
to get the algebraists out there awake.

>Moreover, all *such* semicircles that cross a given p/q (on the real axis),
>have radii 1/(2*q^2*k + d), k running through all integers.
>But d is not necessarily integer.

Well, it  turned out that it is, indeed. d is a q * e,
with gcd (e, 2 * q) = 1. There's obviously a bijection
between these e's and the p's with gcd (p, q) = 1.
But I couldn't find an explicit formula for this.

>Any suggestions and hints to the literature would be appreciated.

Johannes Waldmann,

[e-mail] -- currently: [e-mail]