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Arithmetic of the modular function j 1 , 4

Chang Heon Kim, Ja Kyung Koo (1998)

Acta Arithmetica

We find a generator j 1 , 4 of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator N ( j 1 , 4 ) which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.

Arithmetically Gorenstein curves on arithmetically Cohen-Macaulay surfaces.

Alberto Dolcetti (2002)

Collectanea Mathematica

Let Sigma C PN be a smooth connected arithmetically Cohen-Macaulay surface. Then there are at most finitely many complete linear systems on Sigma, not of the type |kH - K| (H hyperplane section and K canonical divisor on Sigma), containing arithmetically Gorenstein curves.

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