Linear Equations in Singular Moduli
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DOI: 10.1093/imrn/rny216
Abstract: We establish an effective version of the André–Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. This gives the first effective nontrivial results of André–Oort type for higher-dimensional varieties in products of modular curves. read more here.
Keywords: equations singular; singular moduli; linear equations;
Equations with powers of singular moduli
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DOI: 10.1142/s1793042119500234
Abstract: We treat two different equations involving powers of singular moduli. On the one hand, we show that, with two possible (explicitly specified) exceptions, two distinct singular moduli [Formula: see text] such that the numbers [Formula:… read more here.
Keywords: powers singular; formula see; see text; singular moduli ... See more keywords
Singular moduli for real quadratic fields: A rigid analytic approach
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DOI: 10.1215/00127094-2020-0035
Abstract: A rigid meromorphic cocycle is a class in the rst cohomology of the discrete group Γ := SL2(Z[1/p]) with values in the multiplicative group of non-zero rigid meromorphic functions on the p-adic upper half plane… read more here.
Keywords: moduli real; singular moduli; rigid meromorphic; fields rigid ... See more keywords