Special values of generalized $λ$ functions at imaginary quadratic points

Details Special values of generalized $λ$ functions at imaginary quadratic points Special values of generalized $λ$ functions at imaginary quadratic points

2011-10-29

arxiv.org/abs/1110.6489v1

Mathematics

Number Theory

In this paper, we generalize the results in the paper(arXiv:1110.4429v1[math.NT]20 Oct 2011)

Scientific paper

We study a modular function $\Lambda_{k,\ell}$ which is one of generalized $\lambda$ functions. We show $\Lambda_{k,\ell}$ and the modular invariant function $j$ generate the modular function field with respect to the modular subgroup $\Gamma_1(N)$. Further we prove that $\Lambda_{k,\ell}$ is integral over $\mathbf Z[j]$. From these results, we obtain that the value of $\Lambda_{k,\ell}$ at an imaginary quadratic point is an algebraic integer and generates a ray class field over the Hilbert class field.

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