Surya Ramana (Harish Chandra Mathematical Research Institute, Allahabad,
India):
Additive Energy of Dense Sets of Primes and
Monochromatic Sums
<br>(joint work with with Olivier Ramare)
<br><br>
Abstract :
When $K\geq 1$ is an integer and S is a set of prime numbers in the
interval (N/2, N] with more than 1/K of the primes in this interval,
we obtain an upper bound for the additive energy of this set of
primes S, The bound is obtained by a modification of a method of
Ramare and Ruzsa.
By an argument of Hegyvari and Hennecart, this bound implies that
when the set of prime numbers is coloured with K colours, every
sufficiently large integer can be expressed as the sum of CK\log \log
K monochromatic primes. This last assertion is optimal in  its
dependence on $K$.