Xuancheng Shao

A density version of the Vinogradov three primes theorem

We prove that if A is a subset of the primes, and the lower density of A in the primes is larger than 5/8, then all sufficiently large odd positive integers can be written as the sum of three primes in A. The constant 5/8 in this statement is the best possible.

Vinogradov's three primes theorem with almost twin primes

In this paper we prove two results concerning Vinogradovs three primes theorem with primes that can be called almost twin primes. First, for any

Carries, Group Theory, and Additive Combinatorics

m

On character sums and exponential sums over generalized arithmetic progressions

, every sufficiently large odd integer

SMOOTH-SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE

N

x^{1/2}

can be written as a sum of three primes

-BARRIER

p_1, p_2

On an inverse ternary Goldbach problem

and

Weyl sums, mean value estimates, and Waring's problem with friable numbers

p_3

Vinogradov's theorem with almost equal summands

such that, for each