In Theorem 2 of the paper "A polynomial divisor problem" by Friedlander and Iwaniec, Theorem 2 states that $$\sum\_{a^6 + b^2\le x} \Lambda(a^6 + b^2)\sim cx^{2/3}$$ for some constant $c > 0$ (in the paper itself, they give a precise error term and make $c$ explicit).


They then say that "The proof of Theorem 2 will be given elsewhere." Where is this proof?



Locating a certain result on primes represented by a certain polynomial
They prove it in section 14 ("An Application") of their paper


* John Friedlander & Henryk Iwaniec, "The Illusory Sieve" (2005)


As pointed out by Lucia in the comments, the result is conditional on the existence of exceptional characters, an hypothesis which is generally not expected to hold.


