do all power series with coefficients $a_n \in c.e.$ set converge and be represented as automorphic function?

do all power series with coefficients $a_n \in c.e.$ set converge and be represented as automorphic function? [closed]

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given any c.e.set S outputed by an partially computable function $f(n)$, a power series F in the form $F=\Sigma_0^{\infty} a_n x^n$ corresponding to the set S,whose coefficient $a_n=f(n)$ if $f(n)$ is defined,otherwise $a_n=0$. when does F be an automorphic function?

edited Oct 28 2011 at 18:58

asked Oct 28 2011 at 18:43

XL
379●1●7

You should explain how to get $a_n$ from $S$ (there are several ways). Which group action should $F$ be invariant under? Also, and perhaps most important, why in the world are you thinking about this? – François G. Dorais♦ Oct 28 2011 at 18:49

Thank you Francois,for your comment – XL Oct 28 2011 at 18:59

I just require that $F$ is automorphic function,if $F$ has restriction on automorphic function,that will be better result. – XL Oct 28 2011 at 19:03

I am thinking about this just for fun?Maybe,but I guess there must be some connection between invariation or periodicity and computability – XL Oct 28 2011 at 19:06

please comment before downvoting. – XL Oct 28 2011 at 19:16

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closed as not a real question by Qiaochu Yuan, David Loeffler, Felipe Voloch, GH, François G. Dorais♦ Oct 29 2011 at 5:51

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