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A Calculation of the Number of Lattice Points in the Circle and Sphere
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fraser, W. Gotlieb, Calvin C. |
| Copyright Year | 1962 |
| Abstract | (3) V x) = Hx P (k/2 + 1) P2(x) has been investigated by many celebrated mathematicians and Wilton [11 gives an account of the early work. More recently there have been theoretical investigations of Pk(X) for higher dimensions, particularly by Walfisz [2], whose notation is being followed here. We write P2(x) = O(xc) to mean, in the usual sense, that there exists K such that I P2(x) L/xc 0, and a sequence of values of x tending to infinity, for which I P2(x) I/xc > K that is, the negation of P2(x) = o(xc). Gauss observed that P2(x) = 0(X1/2) Hua [3] has shown that P2(X) = 0(x 1340), |
| Starting Page | 282 |
| Ending Page | 290 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0025-5718-1962-0155788-9 |
| Alternate Webpage(s) | http://www.ams.org/journals/mcom/1962-16-079/S0025-5718-1962-0155788-9/S0025-5718-1962-0155788-9.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0025-5718-1962-0155788-9 |
| Volume Number | 16 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
