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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

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Looking for Direction on algebraic and transcendental functions

My question really is: if $e^{2\pi i* g(\theta)}$ is an algebraic function in the variable $e^{2 \pi i \theta}$, what restrictions can we put on g? My first guess is to say that g is the map that …
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