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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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j-invariant fixed point?
If there exists a fixed point for $j\(\tau\)$ then the modularity of $j$ will demand that there exist a lattice of fixed points. Since any point in the complex plane is an image of $j$ this is not pos …