Modular polynomials on Hilbert surfaces
From MaRDI portal
Publication:784730
DOI10.1016/j.jnt.2020.04.014zbMath1456.11078OpenAlexW2613429502MaRDI QIDQ784730
Publication date: 3 August 2020
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jnt.2020.04.014
modular polynomialsabelian surfacetheta constantcyclic isogenyHumbert surfacemoduli space of Hilbert and Siegel
Algebraic number theory computations (11Y40) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)
Related Items (4)
Degree and height estimates for modular equations on PEL Shimura varieties ⋮ Cyclic Isogenies for Abelian Varieties with Real Multiplication ⋮ Computing the 2-adic canonical lift of genus 2 curves ⋮ Generalized class polynomials
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- K3 surfaces and equations for Hilbert modular surfaces
- Explicit CM theory for level 2-structures on abelian surfaces
- Isogeny graphs of ordinary abelian varieties
- Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
- Hilbertsche Modulformen und Modulfunktionen zu \({\mathbb{Q}}(\sqrt{5})\) (Hilbert modular forms and modular functions for \({\mathbb{Q}}(\sqrt{5})\))
- Cryptographic hash functions from expander graphs
- Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves
- On the ring of Hilbert modular forms over \(\mathbb Z\)
- On the geometry of a Siegel modular threefold
- Factoring polynomials with rational coefficients
- On Gröbner bases under specialization
- On the stability of Gröbner bases under specializations
- On the graded ring of Hilbert modular forms associated with \(Q (\sqrt 5)\)
- Hilbertsche Modulformen und Modulfunktionen zu \(Q(\sqrt{8})\)
- Counting points on elliptic curves over finite fields
- Computing the number of points on an elliptic curve over a finite field: algorithmic aspects
- Endomorphism rings of abelian surfaces and projective models of their moduli spaces
- Computing genus 2 curves from invariants on the Hilbert moduli space
- An elliptic curve trapdoor system
- Elliptic periods for finite fields
- Endomorphisms of Abelian varieties over finite fields
- Compactification of arithmetic quotients of bounded symmetric domains
- Die Bestimmung der Funktionen zur Hilbertschen Modulgruppe des Zahlkörpers \(Q(\sqrt 5)\)
- Le problème des groupes de congruence pour \(SL_2\)
- Arithmetic variety of moduli for genus two
- Lectures on Hilbert Modular Varieties and Modular Forms
- Computing Igusa class polynomials
- Computing Class Polynomials for Abelian Surfaces
- Computing theta functions in quasi-linear time in genus two and above
- Fast evaluation of modular functions using Newton iterations and the AGM
- Hilbert Modular Forms and Their Applications
- Computing modular polynomials in quasi-linear time
- Computing Hilbert class polynomials with the Chinese remainder theorem
- Modular Polynomials for Genus 2
- A quasi-linear time algorithm for computing modular polynomials in dimension 2
- Modular Varieties with Level 2 Theta Structure
- Computing Jacobi’s theta in quasi-linear time
- Humbert surfaces and the Kummer plane
- Class Invariants by the CRT Method
- Cyclic Isogenies for Abelian Varieties with Real Multiplication
- An Analysis of Goubin’s Refined Power Analysis Attack
- Modular polynomials via isogeny volcanoes
- An LLL-reduction algorithm with quasi-linear time complexity
- Fast genus 2 arithmetic based on Theta functions
- The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
- Modular Forms and Projective Invariants
- Die Bestimmung der Funktionen zu einigen Hilbertschen Modulgruppen.
- Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
- Public Key Cryptography - PKC 2006
This page was built for publication: Modular polynomials on Hilbert surfaces
