L-series and their 2-adic valuations at s = 1 attached to CM elliptic curves
Lucas' square pyramid problem revisited
Matrix divisibility sequences
Mean-periodicity and zeta functions
This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape is shown...
Minorations de formes linéaires de logarithmes elliptiques
Mock Heegner Points and Congruent Numbers.
Modular automorphisms of the Drinfeld modular curves X0 (n).
Modular parametrizations of certain elliptic curves
Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings.
Modulární křivky a Fermatova věta
Modules de Swan et courbes elliptiques à multiplication complexe
Mordell-Weil lattices in characteristic 2. III: A Mordell-Weil lattice of rank 128.
Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples
We study the family of elliptic curves y² = x(x-a²)(x-b²) parametrized by Pythagorean triples (a,b,c). We prove that for a generic triple the lower bound of the rank of the Mordell-Weil group over ℚ is 1, and for some explicitly given infinite family the rank is 2. To each family we attach an elliptic surface fibered over the projective line. We show that the lower bounds for the rank are optimal, in the sense that for each generic fiber of such an elliptic surface its corresponding Mordell-Weil...
No -torsion on elliptic curves over cubic number fields
We complete our previous determination of the torsion primes of elliptic curves over cubic number fields, by showing that is not one of those.
Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture
Nonvanishing of L-functions and structure of Mordell-Weil groups.
Non-vanishing of -th derivatives of twisted elliptic -functions in the critical point
Let be a modular elliptic curve over
Nonvanishing theorems for L-functions of modular forms and their derivatives.
Note on a product formula for the Bayad function and a law of quadratic reciprocity
Note sur quelques équations indéterminées du troisième degré
Nouvelles approches du «théorème» de Fermat