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Algorithms on Ideal over Complex Multiplication order
Gentry-Szydlo algorithm cyclotomic orders,
2016/3/1
We show in this paper that the Gentry-Szydlo algorithm for cyclotomic orders, previously
revisited by Lenstra-Silverberg, can be extended to complex-multiplication (CM) orders, and
even to a more ge...
Several results point to deep relations between noncommutative geometry and class eld theory ([3],
[10], [20], [22]). In [3] a quantum statistical mechanical system (BC) is exhibited, with partition...
POWER RESIDUES OF FOURIER COEFFICIENTS OF ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION
Elliptic curve a prime number parathyroid hormone Fourier coefficient
2014/12/24
Fix m greater than one and let E be an elliptic curve over Q with complex multiplication. We formulate conjectures on the density of primes p (congruent to one modulo m) for which the pth Fourier coef...
NON-CYCLIC SUBGROUPS OF JACOBIANS OF GENUS TWO CURVES WITH COMPLEX MULTIPLICATION
Jacobians hyperelliptic curves embedding degree complex multiplication
2009/6/2
Let E be an elliptic curve de ned over a nite eld. Balasubramanian
and Koblitz have proved that if the `th roots of unity ` is not contained
in the ground eld, then a eld extension of the groun...
EMBEDDING DEGREE OF HYPERELLIPTIC CURVES WITH COMPLEX MULTIPLICATION
Jacobians hyperelliptic curves complex multiplication cryptography
2008/8/28
Consider the Jacobian of a genus two curve defined over a finite
field and with complex multiplication. In this paper we show that if the e-Sylow
subgroup of the Jacobian is not cyclic, then the emb...