Abstract. For K3 surfaces, we derive some conditions the characteristic polynomial of the Frobenius on the ´etale cohomology must satisfy. These conditions may be used to speed up...
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between ellip...
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...
Abstract. We show that a specific even unimodular lattice of dimension 80, first investigated by Schulze-Pillot and others, is extremal (i.e., the minimal nonzero norm is 8). Thi...
: We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root r and an integer t in the interval [1, p − 1] with logr t = t. Here, logr is the d...
Abstract. We answer a question asked by Hajdu and Tengely: The only arithmetic progression in coprime integers of the form (a2 , b2 , c2 , d5 ) is (1, 1, 1, 1). For the proof, we ...