11 citations · 35 across the 8 of their papers we have counts for
11 papers
Homogeneous Forms Inequalities
Faustin Adiceam, Oscar Marmon
Given a set of inequalities determined by homogeneous forms, the following intertwined results are established: (1) the volume of the real semi-algebraic domain determined by these…
Rational points close to non-singular algebraic curves
Faustin Adiceam, Oscar Marmon
We study the density of solutions to Diophantine inequalities involving non-singular ternary forms, or equivalently, the density of rational points close to non-singular plane alge…
On the Hasse principle for quartic hypersurfaces
Oscar Marmon, Pankaj Vishe
We establish the Hasse principle for smooth projective quartic hypersurfaces of dimension greater than or equal to 28 defined over .
Diophantine equations in moderately many variables
Oscar Marmon
We give upper bounds for the number of integral solutions of bounded height to a system of equations , , where the are polynomials w…
Random Thue and Fermat equations
Rainer Dietmann, Oscar Marmon
We consider Thue equations of the form , and assuming the truth of the -conjecture, we show that almost all locally soluble Thue equations of degree at least th…
The density of twins of -free numbers
Rainer Dietmann, Oscar Marmon
For , we consider the number of positive integers such that both and are -free. We prove an asymptotic formula $A_k(Z) = c_k Z + O(Z^{14/…