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Preprints, Working Papers, ... Year : 2016

Schertz style class invariants for quartic CM fields

Abstract

A class invariant is a CM value of a modular function that lies in a certain unram-ified class field. We show that Siegel modular functions over $Q$ for $Γ^0 (N) ⊆ Sp_4 (Z)$yield class invariants under some splitting conditions on N. Small class invariants speed up constructions in explicit class field theory and public-key cryptography. Our results generalise results of Schertz's from elliptic curves to abelian varieties and from classical modular functions to Siegel modular functions.
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Dates and versions

hal-01377376 , version 1 (10-10-2016)
hal-01377376 , version 2 (28-05-2021)

Identifiers

  • HAL Id : hal-01377376 , version 2

Cite

Andreas Enge, Marco Streng. Schertz style class invariants for quartic CM fields. 2016. ⟨hal-01377376v2⟩
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