A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points in an expanding box at which given rational forms of the same degree simultaneously vanish, subject to a geometric condition. We present the first inequalities analogue of Birch’s theorem
For any $n \geq 2$, let $F \in \mathbb{Z}[x_1,\ldots,x_n]$ be a form of degree $d\geq 2$, which prod...
In this article, we develop the convergence theory of simultaneous, inhomogeneous Diophantine approx...
Let C be a cubic form with integer coefficients in n variables, and let h be the h-invariant of C. L...
A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points ...
Let F_1,\ldots ,F_R be quadratic forms with integer coefficients in n variables. When n\ge 9R and th...
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which t...
We consider a system of R cubic forms in n variables, with integer coefficients, which define a smoo...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
We study the number of representations of an integer n=F(x) by a homogeneous form in sufficiently ma...
This thesis is concerned with establishing Manin's conjecture on the distribution of ratinal points ...
In this thesis we study several problems related to the representation of integers by binary forms a...
For any integers $d,n \geq 2$, let $X \subset \mathbb{P}^{n}$ be a non-singular hypersurface of deg...
Let n be a positive multiple of 4. We establish an asymptotic formula for the number of rational poi...
We consider systems of polynomial equations and inequalities to be solved in integers. By applying t...
For any $n \geq 2$, let $F \in \mathbb{Z}[x_1,\ldots,x_n]$ be a form of degree $d\geq 2$, which prod...
In this article, we develop the convergence theory of simultaneous, inhomogeneous Diophantine approx...
Let C be a cubic form with integer coefficients in n variables, and let h be the h-invariant of C. L...
A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points ...
Let F_1,\ldots ,F_R be quadratic forms with integer coefficients in n variables. When n\ge 9R and th...
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which t...
We consider a system of R cubic forms in n variables, with integer coefficients, which define a smoo...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
We study the number of representations of an integer n=F(x) by a homogeneous form in sufficiently ma...
This thesis is concerned with establishing Manin's conjecture on the distribution of ratinal points ...
In this thesis we study several problems related to the representation of integers by binary forms a...
For any integers $d,n \geq 2$, let $X \subset \mathbb{P}^{n}$ be a non-singular hypersurface of deg...
Let n be a positive multiple of 4. We establish an asymptotic formula for the number of rational poi...
We consider systems of polynomial equations and inequalities to be solved in integers. By applying t...
For any $n \geq 2$, let $F \in \mathbb{Z}[x_1,\ldots,x_n]$ be a form of degree $d\geq 2$, which prod...
In this article, we develop the convergence theory of simultaneous, inhomogeneous Diophantine approx...
Let C be a cubic form with integer coefficients in n variables, and let h be the h-invariant of C. L...
DOI
Add to ORKG