Sure monochromatic subset sums
Taille des valeurs de fonctions L de carrés symétriques au bord de la bande critique.
Ternary quadratic forms with rational zeros
We consider the Legendre quadratic formsand, in particular, a question posed by J–P. Serre, to count the number of pairs of integers , for which the form has a non-trivial rational zero. Under certain mild conditions on the integers , we are able to find the asymptotic formula for the number of such forms.
The additive complements of primes and Goldbach's problem
We extend two results of Ruzsa and Vu on the additive complements of primes.
The binary Goldbach problem with arithmetic weights attached to one of the variables
The circle method and pairs of quadratic forms
We give non-trivial upper bounds for the number of integral solutions, of given size, of a system of two quadratic form equations in five variables.
The EKG sequence.
The Erdhős-Kac Theorem for Curvatures in Integral Apollonian Circle Packings
The Goldston-Pintz-Yıldırım sieve and maximal gaps
The greatest prime factor of the integers in an interval
The k-tuple jumping champions among consecutive primes
The largest prime factor of X³ + 2
Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .
The least prime primitive root and the shifted sieve
The level of distribution of the special values of L-functions
The multiplicative group of rationals generated by the shifted primes, I.
The polynomial captures its primes.
The Romanoff theorem revisited
The Rosser-Iwaniec sieve in number fields, with an application
The spectral mean value for linear forms in twisted coefficients of cusp forms
Triangular numbers whose sum of divisors is also triangular