Counting solutions of decomposable form equations
Counting with Gauss' sums.
Courbes modulaires et courbes de Fermat.
Criterion for 3 to be eleventh power
Crossed ladders and Euler's quartic.
Cubic forms, powers of primes and the Kraus method
We consider the Diophantine equation , where B, D are integers (B ≠ ±2, D ≠ 0) and p is a prime >5. We give Kraus type criteria of nonsolvability for this equation (explicitly, for many B and D) in terms of Galois representations and modular forms. We apply these criteria to numerous equations (with B = 0, 1, 3, 4, 5, 6, specific D’s, and p ∈ (10,10⁶)). In the last section we discuss reductions of the above Diophantine equations to those of signature (p,p,2).
Cubic moments of Fourier coefficients and pairs of diagonal quartic forms
We establish the non-singular Hasse principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensional 21st moment of quartic smooth Weyl sums via a novel cubic moment of Fourier coefficients.
Darstellung natürlicher Zahlen als Summe von Quadraten
Decomposable form equations with a small linear scattering.
Décomposition du carré d’un nombre et de ce nombre lui-même en sommes quadratiques de la forme étant un nombre rationnel, positif ou négatif ; résolution en nombres entiers du système des équations indéterminées
Décomposition du carré d’un nombre N et de ce nombre lui-même en sommes quadratiques de la forme étant un nombre rationnel positif ou négatif ; résolution en nombres entiers du système des équations indéterminées
Decomposition of an integer as a sum of two cubes to a fixed modulus
Deformations of Diophantine systems for quadratic forms of the root lattices .
Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch
A nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the...
Démonstration des propositions de M. Lionnet
Démonstration d'un théorème de Fermat
Denser Egyptian fractions
Density of rational points on cyclic covers of
We obtain upper bound for the density of rational points on the cyclic covers of . As our estimate tends to the conjectural bound of Serre.
Density of rational points on elliptic fibrations
Density of rational points on elliptic fibrations-II