Counting sums of two squares: the Meissel-Lehmer method-Reference-Cited by-同舟云学术

Counting sums of two squares: the Meissel-Lehmer method

Published:1986 Issue:175 Volume:47 Page:351-360
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Shiu P.

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 ) 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 ) W(x) and use it to calculate W ( 10 12 ) W({10^{12}}) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1986-47-175/S0025-5718-1986-0842141-1/S0025-5718-1986-0842141-1.pdf

Reference8 articles.

1. London Mathematical Society Monographs, No. 4;Halberstam, H.,1974

2. The lattice-points in a circle;Hua, Loo-keng;Quart. J. Math. Oxford Ser.,1942

3. Experiments on the lattice problem of Gauss;Keller, H. B.;Math. Comp.,1963

4. Computing 𝜋(𝑥): the Meissel-Lehmer method;Lagarias, J. C.;Math. Comp.,1985

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Corrigendum to “Counting sums of two squares: the Meissel-Lehmer method”;Mathematics of Computation;2019-06-27

2. The gaps between sums of two squares;The Mathematical Gazette;2013-07

3. The First Years;Springer Monographs in Mathematics;2012

4. Good Rotations;Journal of Computational Physics;1998-10