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5 papers · 1 filter
Modular elliptic directions with complex multiplication (with an application to Gross's elliptic curves)
Josep Gonzalez, Joan-C. Lario
For every normalized newform f in S_2(Gamma_1(N)) with complex multiplication, we study the modular parametrizations of elliptic curves C from the abelian variety A_f. We apply the…
Square-free discriminants of Frobenius rings
Chantal David, Jorge Jimenez Urroz
Let be an elliptic curve over $\Q$. It is well known that the ring of endomorphisms of , the reduction of modulo a prime of ordinary reduction, is an order of the…
Small primitive roots and malleability of RSA moduli
Luis Dieulefait, Jorge Jimenez Urroz
In a paper of P. Paillier and J. Villar a conjecture is made about the malleability of an RSA modulus. In this paper we present an explicit algorithm refuting the conjecture. Concr…
On the critical pair theory in Z/pZ
Yahya Ould Hamidoune, Oriol Serra, Gilles Zemor
Let A and B be subsets of Z/pZ such that |A+B| < |A|+|B|+2. We prove that, if |A|>3, |B|>4, |A+B|<p-4 and p > 52, then A and B are included in arithmetic progressions with the same…
Quaternions, polarizations and class numbers
Victor Rotger
We study abelian varieties with multiplication by a totally indefinite quaternion algebra over a totally real number field and give a criterion for the existence of principal p…