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A Gross-Zagier formula for quaternion algebras over totally real fields
public-key cryptography hyperelliptic curve cryptosystem
2012/6/14
We prove a higher dimensional generalization of Gross and Zagier's theorem on the factorization of differences of singular moduli. Their result is proved by giving a counting formula for the number of...
A Gross-Zagier formula for quaternion algebras over totally real fields
public-key cryptography hyperelliptic curve cryptosystem
2012/3/20
We prove a higher dimensional generalization of Gross and Zagier's theorem on the factorization of differences of singular moduli. Their result is proved by giving a counting formula for the number of...
A Gross-Zagier formula for quaternion algebras over totally real fields
public-key cryptography hyperelliptic curve cryptosystem
2012/8/28
We prove a higher dimensional generalization of Gross and Zagier's theorem on the factorization of differences of singular moduli. Their result is proved by giving a counting formula for the number of...
Liftings of Reduction Maps for Quaternion Algebras
Liftings of Reduction Maps Quaternion Algebras
2011/1/18
We construct liftings of reduction maps from CM points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefin...
On the conjugacy of pure imaginary elements of quaternion algebras and Cayley algebras
quaternion algebras Cayley algebras
2010/11/9
In the quatenions ($\H$, $\H'$, $\H^{C}$) and octonions ($\gC$, $\gC^\prime$, $\gC^C$), we show some results on the conjugacy of two pure imaginary non-zero elements with same norm.