32 citations · 42 across the 6 of their papers we have counts for
6 papers
Quadratic residue patterns and point counting on K3 surfaces
Valentina Kiritchenko, Mikhail Tsfasman, Serge Vladuts +1
Quadratic residue patterns modulo a prime are studied since 19th century. We state the last unpublished result of Lydia Goncharova, reformulate it and prior results in terms of alg…
Some remarks on Heath-Brown's theorem on quadratic forms
Andrey Dymov, Sergei Kuksin, Alberto Maiocchi +1
In his paper from 1996 on quadratic forms Heath-Brown developed a version of circle method to count points in the intersection of an unbounded quadric with a lattice of short perio…
Singular solutions of conformal Hessian equation
Nikolai Nadirashvili, Serge Vladuts
We show that for any there exists an analytic outside zero solution to a uniformly elliptic conformal Hessian equation in a ball which belongs to $C^{1,…
Singular Solutions of Hessian Elliptic Equations in Five Dimensions
Nikolai Nadirashvili, Serge Vladuts
We show that for any there exists a homogeneous order analytic outside zero solution to a uniformly elliptic Hessian equation in R^5.
Nonclassical Solutions of Fully Nonlinear Elliptic Equations II. Hessian Equations and Octonions
Nikolai Nadirashvili, Serge Vladuts
We use the octonion algebra to construct singular solutions of Hessian fully nonlinear uniformly elliptic equations in 21 or more dimensions. The regularity of these solutions is t…
Singular Solution to Special Lagrangian Equations
Nikolai Nadirashvili, Serge Vladuts
We prove the existence of non-smooth solutions to Special Lagrangian Equations in the non-convex case.