The paper asserts that ring class fields of real quadratic fields Q(√p) for primes p ≡ 3 mod 4 are contained in coefficient fields of certain modular forms, but the proof is incomplete and contradicts its own p=7 example.
Measured foliations and Hilbert 12th problem
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abstract
Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are generated by the pseudo-lattices with real multiplication. We prove this conjecture using theory of measured foliations on the modular curves.
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Addendum to "Measured foliations and Hilbert 12th problem"
The paper asserts that ring class fields of real quadratic fields Q(√p) for primes p ≡ 3 mod 4 are contained in coefficient fields of certain modular forms, but the proof is incomplete and contradicts its own p=7 example.