The Polynomial X 2 + Y 4 Captures Its Primes

This article proves that there are infinitely many primes of the form a^2 + b^4, in fact getting the asymptotic formula. The main result is that ∑a^2 + b^4≤ x Λ(a^2 + b^4) = 4π⁻¹κ x3/4 (1 + O(loglog x / log x)) where a, b run over positive integers and κ = ∫^1_0 (1 - t^4)1/2 dt = Γ(1/4)^2 /6√2π. Here of course, Λ denotes the von Mangoldt function and Γ the Euler gamma function.