Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583272 | Finite Fields and Their Applications | 2008 | 17 Pages |
Abstract
Let q=pr with p=3 and r⩾2. We give a recursion formula for the moments of a Kloosterman sum over the finite field Fq, which utilizes known weight formulae for the ternary Melas code M of length q−1. The method is illustrated by giving explicit formulae for the moments up to the tenth moment. As an application for the formulae, and for their analogues obtained earlier in case p=2, we get the exact number of rational points on fibre products of certain Kloosterman curves. As a corollary we obtain identities between Ramanujan's tau-function, Kronecker class numbers, and Dickson polynomials.
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