The Schnirelmann density of the sums of three squares
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- by Samuel S. Wagstaff
- Proc. Amer. Math. Soc. 52 (1975), 1-7
- DOI: https://doi.org/10.1090/S0002-9939-1975-0379425-4
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Abstract:
The number in the title is $5/6$, which is the same as the asymptotic density of the set. The best possible upper and lower bounds (of the form $5x/6 + A + B\log x$) are obtained for the number of positive integers less than $x$ which are a sum of three squares.References
- E. Landau, Elementare Zahlentheorie, Teubner, Leipzig, 1927; English transl., Elementary number theory, Chelsea, New York, 1958. MR 19, 1159.
—, Über die Einteilung der positiven ganzen Zahlen in vier Klassen nach der Mindestzahl der zu ihrer additiven Zusammensetzung erforderlichen Quadrate, Arch. Math. Phys. 13 (1908), 304-312.
S. Ramanujan, On the expression of a number in the form $a{x^2} + b{y^2} + c{z^2} + d{u^2}$, Proc. Cambridge Philos. Soc. 19 (1917), 11-21.
- Kenneth Rogers, The Schnirelmann density of the squarefree integers, Proc. Amer. Math. Soc. 15 (1964), 515–516. MR 163893, DOI 10.1090/S0002-9939-1964-0163893-X
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 1-7
- MSC: Primary 10L10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0379425-4
- MathSciNet review: 0379425