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...
Lattice points in a circle: An improved mean-square asymptotics
Le crible à vecteurs
Le plus grand facteur premier de n² + 1 où est presque premier
L'ensemble exceptionnel dans la conjecture de Szpiro
Levels of Distribution and the Affine Sieve
We discuss the notion of a “Level of Distribution” in two settings. The first deals with primes in progressions, and the role this plays in Yitang Zhang’s theorem on bounded gaps between primes. The second concerns the Affine Sieve and its applications.
Linear equations with the Euler totient function
Lower and upper bounds for the number of solutions of
Lower bounds for sums of Barban-Davenport-Halberstam type.