The binary Goldbach problem with arithmetic weights attached to one of the variables
The Bouniakowsky conjecture and the density of polynomial roots to prime moduli
The Chen primes contain arbitrarily long arithmetic progressions
The divisor problem for binary cubic forms
We investigate the average order of the divisor function at values of binary cubic forms that are reducible over and discuss some applications.
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 polynomial captures its primes.
The representation of primes by cubic polynomials
The representation of primes by quadratic and cubic polynomials