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The number of primes representable as the sum of two square-free squares
Published online by Cambridge University Press: 20 January 2009
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In this paper an asymptotic formula is obtained for the number of primes representable as the sum of two square-free squares. The precise result is:
Theorem 1.Let N(x) be the number of primes not exceeding x represented by the quadratic formy2 + z2, where y and z are square-free. Let w be a fixed arbitrarily large number. Then
where
and
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- Copyright © Edinburgh Mathematical Society 1976