We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work of Birch. To do so, we use a variant of Bourgain’s arithmetic version of the Tomas–Stein method and Magyar’s decomposition of the Fourier transform of the indicator function of the integer points on a hypersurface
We apply Christ’s method of refinements to the ℓ^p-improving problem for discrete averages AN along ...
We study the number of representations of an integer n=F(x) by a homogeneous form in sufficiently ma...
We prove new Fourier restriction estimates to the unit sphere $\mathbb{S}^{d-1}$ on the class of $O(...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
We prove a maximal Fourier restriction theorem for hypersurfaces in (mathbb{R}^{d}) for any dimensio...
We will present new restriction estimates for surfaces of finite type. We give the sharp Lp-Lq estim...
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which t...
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...
In this article we establish two new results on quantitative Diophantine approximation for one-param...
Let C be the boundary surface of a strictly convex d-dimensional body. Andrews obtained an upper bou...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
Estimating averages of Dirichlet convolutions1 * $X" , for some real Dirichlet character $X$ of fixe...
The main result of this note is the strengthening of a quite arbitrary a priori Fourier restriction ...
We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This ...
We apply Christ’s method of refinements to the ℓ^p-improving problem for discrete averages AN along ...
We study the number of representations of an integer n=F(x) by a homogeneous form in sufficiently ma...
We prove new Fourier restriction estimates to the unit sphere $\mathbb{S}^{d-1}$ on the class of $O(...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
We prove a maximal Fourier restriction theorem for hypersurfaces in (mathbb{R}^{d}) for any dimensio...
We will present new restriction estimates for surfaces of finite type. We give the sharp Lp-Lq estim...
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which t...
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...
In this article we establish two new results on quantitative Diophantine approximation for one-param...
Let C be the boundary surface of a strictly convex d-dimensional body. Andrews obtained an upper bou...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
Estimating averages of Dirichlet convolutions1 * $X" , for some real Dirichlet character $X$ of fixe...
The main result of this note is the strengthening of a quite arbitrary a priori Fourier restriction ...
We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This ...
We apply Christ’s method of refinements to the ℓ^p-improving problem for discrete averages AN along ...
We study the number of representations of an integer n=F(x) by a homogeneous form in sufficiently ma...
We prove new Fourier restriction estimates to the unit sphere $\mathbb{S}^{d-1}$ on the class of $O(...
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