Hellus, Michael and Waldi, Rolf (2015) INTERPOLATION IN AFFINE AND PROJECTIVE SPACE OVER A FINITE FIELD. JOURNAL OF COMMUTATIVE ALGEBRA, 7 (2). pp. 207-219. ISSN 1939-0807, 1939-2346
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | REGULARITY; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Michael Hellus |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 Jul 2019 13:06 |
| Last Modified: | 11 Jul 2019 13:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/5375 |
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