Abstract
Coordinate distribution of Gaussian primes
Highlights
In [FrIw1], the current authors obtained the asymptotic in the setting where one of the squares was the square of a square and for the number of primes which could be written as the sum of a square plus a fourth power
This result had an additional interest in first successfully establishing the asymptotic formula for a thin set of prime values of a polynomial, that is, one having density ≪ x1−δ for some positive δ
Li [HL] have shown that, in the statement of [FrIw1], one can replace the fourth power of an integer by the fourth power of a prime and still establish for these the relevant asymptotic formula
Summary
4k2+l2 x it seems only natural to ask what happens when we consider the visually similar sum.
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