Zusammenfassung
Let s(n, q) be the smallest number s such that any n-fold F-q-valued interpolation problem in P-Fq(k) has a solution of degree s, that is: for any pairwise different F-q-rational points P-1,.., P-n there exists a hypersurface H of degree s defined over F-q such that P-1,.., Pn-1 is an element of H and P-n is not an element of H. This function s(n, q) was studied by Kunz and the second author in ...
Zusammenfassung
Let s(n, q) be the smallest number s such that any n-fold F-q-valued interpolation problem in P-Fq(k) has a solution of degree s, that is: for any pairwise different F-q-rational points P-1,.., P-n there exists a hypersurface H of degree s defined over F-q such that P-1,.., Pn-1 is an element of H and P-n is not an element of H. This function s(n, q) was studied by Kunz and the second author in [8] and completely determined for q = 2 and q = 3. For q >= 4, we improve the results from [8]. The affine analogue to s(m, q) is the smallest number s = s (n, q) such that any n-fold F-q-valued interpolation problem in A(k) (F-q), k is an element of N->0 has a polynomial solution of degree <= s. We exactly determine this number.
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