Counting sums of two squares: the Meissel-Lehmer method

Shiu, P.

doi:10.1090/S0025-5718-1986-0842141-1

Counting sums of two squares: the Meissel-Lehmer method
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Math. Comp. 47 (1986), 351-360 Request permission

Corrigendum: Math. Comp. 88 (2019), 2935-2938.

Abstract:

In 1870, E. D. F. Meissel developed a method for computing the individual values of the prime-counting function, and, in 1959, D. H. Lehmer simplified and extended Meissel’s method. Let $W(x)$ count the numbers not exceeding x that are sums of two squares. We develop a variant of the Meissel-Lehmer method for $W(x)$ and use it to calculate $W({10^{12}})$.

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