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A quasi-linear time algorithm for computing modular polynomials in dimension 2. (English) Zbl 1371.11159
Summary: We propose to generalize the work of Régis Dupont [Math. Comput. 80, No. 275, 1823–1847 (2011; Zbl 1221.65075)] for computing modular polynomials in dimension \(2\) to new invariants. We describe an algorithm to compute modular polynomials for invariants derived from theta constants and prove heuristically that this algorithm is quasi-linear in its output size. Some properties of the modular polynomials defined from quotients of theta constants are analyzed. We report on experiments with our implementation.

MSC:
11Y35 Analytic computations
11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
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