Chowla, S. ; Cowles, J. ; Cowles, M. (1977) On the number of zeros of diagonal cubic forms Journal of Number Theory, 9 (4). pp. 502-506. ISSN 0022-314X
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002231...
Related URL: http://dx.doi.org/10.1016/0022-314X(77)90010-5
Abstract
Let Ms, be the number of solutions of the equation X13+ X23+ … + Xs3=0 in the finite field GF(p). For a prime p ≡ 1(mod 3), ∑∞s=1 MsX3 = (x/1-px)+((x2(p-1)(2+dx))/(1-3px2-pdx3)), M3= p2 + d(p - 1), and M4 = p2 + 6(p2 − p). Here d is uniquely determined by 4p = d2 + 27b2 and d ≡ 1(mod 3).
| Item Type: | Article |
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| Source: | Copyright of this article belongs to Elsevier Science. |
| ID Code: | 8605 |
| Deposited On: | 28 Oct 2010 11:20 |
| Last Modified: | 05 Dec 2011 03:59 |
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