Computing Igusa class polynomials
نویسندگان
چکیده
منابع مشابه
Computing Igusa class polynomials
We give an algorithm that computes the genus two class polynomials of a primitive quartic CM field K, and we give a runtime bound and a proof of correctness of this algorithm. This is the first proof of correctness and the first runtime bound of any algorithm that computes these polynomials. Our algorithm uses complex analysis and runs in time e O(∆), where ∆ is the discriminant of K.
متن کاملComputing Igusa Class Polynomials via the Chinese Remainder Theorem
We present a new method for computing the Igusa class polynomials of a primitive quartic CM field. For a primitive quartic CM field, K, we compute the Igusa class polynomials modulo p for certain small primes p and then use the Chinese remainder theorem and a bound on the denominators to construct the class polynomials. We also provide an algorithm for determining endomorphism rings of Jacobian...
متن کاملDenominators of Igusa Class Polynomials
— In [22], the authors proved an explicit formula for the arithmetic intersection number (CM(K).G1) on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field K. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography. One of the...
متن کاملComparing Arithmetic Intersection Formulas for Denominators of Igusa Class Polynomials
Bruinier and Yang conjectured a formula for intersection numbers on an arithmetic Hilbert modular surface, and as a consequence obtained a conjectural formula for CM(K).G1 under strong assumptions on the ramification in K. Yang later proved this conjecture under slightly stronger assumptions on the ramification. In recent work, Lauter and Viray proved a different formula for CM(K).G1 for primit...
متن کاملAn arithmetic intersection formula for denominators of Igusa class polynomials
In this paper we prove an explicit formula for the arithmetic intersection number (CM(K).G1)` on the Siegel moduli space of abelian surfaces, generalizing the work of Bruinier-Yang and Yang. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography. Bruinier and Yang...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2013
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2013-02712-3