Heegner points and Hilbert modular forms
نویسندگان
چکیده
(Here ΛE is a suitable period lattice commensurable with the Néron lattice of E.) The function Φ, which is transcendental as a function of τ , enjoys the following notable algebraicity property, a consequence of the theory of complex multiplication: Theorem HP: Let K ⊂ C be a quadratic imaginary extension of Q, and let K denote its maximal abelian extension. If τ belongs to H ∩ K, then Φ(τ) belongs to E(K). The points in E(K) arising from theorem HP are sometimes called Heegner points (although it is customary to place further restrictions on the values of
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The arithmetic of the values of modular functions and the divisors of modular forms
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