Asymptotics for some polynomial patterns in the primes
Asymptotics for some polynomial patterns in the primes
Abstract We prove asymptotic formulae for sums of the form $$\sum\limits_{n\in {\open z}^d\cap K} {\prod\limits_{i = 1}^t {F_i} } (\psi _i(n)),$$ where K is a convex body, each F i is either the von Mangoldt function or the representation function of a quadratic form, and Ψ = (ψ 1 , …