The polynomial X2+Y4 captures its primes
John Friedlander, Henryk Iwaniec
Abstract
This article proves that there are infinitely many primes of the form a2 + b4, in fact getting the asymptotic formula. The main result is that Σa2 + b4 x Λ(a2 + b4) = 4π-1κx3/4 (1 + O( x / x)) where a, b run over positive integers and κ= ∫10 (1 - t4)1/2 dt = Γ(1/4)2 /62π. Here of course, Λdenotes the von Mangoldt function and Γthe Euler gamma function.
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