Simultaneous diagonal equations over 𝔭-adic fields
Simultaneous p-adic Zeros of Quadratic Forms.
Simultaneous quadratic equations II
Solvability of 𝔭-adic diagonal equations
Some aspects of Davenport's work
Some estimates for diagonal equations over p-adic fields
Some observations on the Diophantine equation f(x)f(y) = f(z)²
Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.
Some Remarks on Vinogradov's Mean Value Theorem and Tarry's Problem.
Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
Sur la dimension diophantienne des corps p-adiques
Sur un problème de Fermat
Symmetric Diophantine systems
Systems of Homogeneous Equations.