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Real multiplication revisited

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arxiv 1404.4999 v3 pith:W5IPSIMK submitted 2014-04-20 math.NT math.OA

Igor Nikolaev This is my paper · ORCID
classification math.NTmath.OA
keywords fieldrealclasscoefficientsconductorcongruenceeigenformfourier
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abstract

It is proved that the Hilbert class field of a real quadratic field ${\Bbb Q}(\sqrt{D})$ modulo a power $m$ of the conductor $f$ is generated by the Fourier coefficients of the Hecke eigenform for a congruence subgroup of level $fD$.

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  1. Addendum to "Measured foliations and Hilbert 12th problem"

    math.NT 2025-05 reject novelty 4.0 of 10

    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.

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