Automorphic Forms by Bernhard Heim Mehiddin Al-Baali Tomoyoshi Ibukiyama & Florian Rupp

Author:Bernhard Heim, Mehiddin Al-Baali, Tomoyoshi Ibukiyama & Florian Rupp
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

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The modular invariant generates the space of weakly modular forms of weight 0, i.e. . It induces a bijection . Let be the discriminant function for

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It is well known that . Moreover, is non-vanishing on . The non-vanishing follows from

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Here the map n ↦ τ(n) is called the Ramanujan function. The discriminant function is a Hecke eigenform with eigenvalues τ(n).

Next we introduce the modular polynomial and its irreducible factors, the primitive modular polynomials . Put

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