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Evaluating modular polynomials in genus 2

Jean Kieffer 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We design algorithms to efficiently evaluate genus 2 modular polyno-mials of Siegel and Hilbert type over number fields, using complex approximations. Under heuristics related to the computation of theta functions in quasi-linear time, the output is provably correct. Our algorithms also apply to finite fields via lifting.
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https://hal.archives-ouvertes.fr/hal-02971326
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Submitted on : Monday, October 19, 2020 - 1:46:00 PM
Last modification on : Saturday, December 4, 2021 - 3:44:00 AM
Long-term archiving on: : Wednesday, January 20, 2021 - 6:45:36 PM

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  • HAL Id : hal-02971326, version 1
  • ARXIV : 2010.10094

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Jean Kieffer. Evaluating modular polynomials in genus 2. 2020. ⟨hal-02971326⟩

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