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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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- Research Article
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- Copyright © Edinburgh Mathematical Society 1976
References
(1) Estermann, T., Introduction to modern prime number theory (Cambridge University Press, 1961).Google Scholar
(2) Keates, M., Sums of squares of square-free numbers, Ph.D. thesis (University of Wales, 1971).Google Scholar
(4) de la Vallée Poussin, C. J., Recherches analytiques sur la théorie des nombrès. Troisieme partie, Annates de la Soc. Sci. de Bruxelles 20 (1896), 363.Google Scholar
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