La «nouvelle technique» de Hooley
Lagrange's Four Squares Theorem with almost prime variables.
Landau’s problems on primes
At the 1912 Cambridge International Congress Landau listed four basic problems about primes. These problems were characterised in his speech as “unattackable at the present state of science”. The problems were the following :(1)Are there infinitely many primes of the form ?(2)The (Binary) Goldbach Conjecture, that every even number exceeding 2 can be written as the sum of two primes.(3)The Twin Prime Conjecture.(4)Does there exist always at least one prime between neighbouring squares?All these...
Large sets with small doubling modulo are well covered by an arithmetic progression
We prove that there is a small but fixed positive integer such that for every prime larger than a fixed integer, every subset of the integers modulo which satisfies and is contained in an arithmetic progression of length . This is the first result of this nature which places no unnecessary restrictions on the size of .
Lattice point problems and distribution of values of quadratic forms.
Lattice point problems and the central limit theorem in Euclidean spaces.
Lattice Point Theory of Irrational Ellipsoids with an Arbitrary Center.
Lattice Points.
Lattice points in a circle: An improved mean-square asymptotics
Lattice Points in a Circle and Divisors in Arithmetic Progressions.
Lattice points in bodies of revolution
Lattice points in bodies with algebraic boundary
Lattice points in ellipsoids
Lattice points in elliptic paraboloids.
Lattice points in four-dimensional tetrahedra and a conjecture of Rademacher.
Lattice Points in High-Dimensional Spheres.
Lattice Points in Large Convex Bodies.
Lattice points in large convex bodies, II
Lattice Points in Lattice Polytopes.
Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary
We investigate the number of lattice points in special three-dimensional convex bodies. They are called convex bodies of pseudo revolution, because we have in one special case a body of revolution and in another case even a super sphere. These bodies have lines at the boundary, where all points have Gaussian curvature zero. We consider the influence of these points to the lattice rest in the asymptotic representation of the number of lattice points.