User junkie - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T13:44:51Z http://mathoverflow.net/feeds/user/31049 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/120369/analytic-function-avoiding-elements-of-the-modular-group/120519#120519 Answer by Junkie for Analytic function avoiding elements of the modular group Junkie 2013-02-01T13:29:42Z 2013-02-01T13:29:42Z <p>I think the idea is the Big Picard theorem.</p> <p>There is a similar problem I think in Halmos (Problems for Mathematicians Young and Old), concerning $z$, $f(z)$, and $f(f(z))$ being always distinct (it is phrased as saying that $f\circ f$ has no fixed points maybe). Then one shows $f$ is a translation. You go by forming the function $g(z)={f(f(z))-z\over f(z)-z}$ or the like, which now omits 0, 1, and $\infty$ from its image. After messing around (consider $g'(z)$ somehow?) this should give the desired result.</p> <p>Your problems seem of a similar flavor.</p> http://mathoverflow.net/questions/120326/on-weils-characters-of-type-a/120330#120330 Answer by Junkie for On Weil's characters of type (A) Junkie 2013-01-30T15:21:55Z 2013-01-30T15:21:55Z <p>Schappacher, Periods of Hecke characters, Chapter Zero, involves some of this, though he quotes SGA 4.5 section 5 for some parts, which could also be useful. I can't track a specific results like what you want, but I think he covers it, in an essence.</p> <p><a href="http://link.springer.com/book/10.1007%2FBFb0082094" rel="nofollow">http://link.springer.com/book/10.1007%2FBFb0082094</a></p>