Chowla, S. (1970) An idea of tate-dwork for the "hasse invariant" applied to a classical theorem of Fermat Journal of Number Theory, 2 (4). pp. 423-424. 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(70)90045-4
Abstract
Let p denote a prime ≡ 1 (mod 4). We have (Fermat) p = a2 + b2 where (say) a ≡ 1 (mod 4). It is proved that α ≡±(1/2)F(p + 1)/2 ( 1/2, 1/2, 1; -1) where Fn(α, β, γ; x) stands for the sum of the first n terms of the hypergeometric series F(α, β, γ; x). The sign is + or − according as p≡ 1 (mod 8) or p ≡ 5 (mod 8).
| Item Type: | Article |
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| Source: | Copyright of this article belongs to Elsevier Science. |
| ID Code: | 8771 |
| Deposited On: | 28 Oct 2010 11:12 |
| Last Modified: | 05 Dec 2011 03:54 |
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