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Concept

Complex multiplication

Related publications (4)

The Lang-Trotter conjecture for products of non-CM elliptic curves

Vlad Serban

Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...

SPRINGER2022

Bilinear forms with Kloosterman sums and applications

Philippe Michel

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Annal Mathematics2017

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Jeanine Marie Van Order

We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...

2012

Generating anomalous elliptic curves

Serge Vaudenay, Jean Monnerat

In 1999, Smart has shown how to solve in linear time ECDLP for elliptic curves of trace 1 defined over a prime finite field Fp, the so-called anomalous elliptic curves. In this article, we show how to construct such cryptographically weak curves for primes ...

2005