Newtonian and Schinzel sequences in a domain |
| |
Authors: | Paul-Jean Cahen |
| |
Institution: | Université Paul Cézanne, LATP CNRS-UMR 6632, Faculté des Sciences et Techniques, 13397 Marseille Cedex 20, France |
| |
Abstract: | A Schinzel or F sequence in a domain is such that, for every ideal I with norm q, its first q terms form a system of representatives modulo I, and a Newton or N sequence such that the first q terms serve as a test set for integer-valued polynomials of degree less than q. Strong F and strong N sequences are such that one can use any set of q consecutive terms, not only the first ones, finally a very well F ordered sequence, for short, a V.W.F sequence, is such that, for each ideal I with norm q, and each integer s,{usq,…,u(s+1)q−1} is a complete set of representatives modulo I. In a quasilocal domain, V.W.F sequences and N sequences are the same, so are strong F and strong N sequences. Our main result is that a strong N sequence is a sequence which is locally a strong F sequence, and an N sequence a sequence which is locally a V.W.F. sequence. We show that, for F sequences there is a bound on the number of ideals of a given norm. In particular, a sequence is a strong F sequence if and only if it is a strong N sequence and for each prime p, there is at most one prime ideal with finite residue field of characteristic p. All results are refined to sequences of finite length. |
| |
Keywords: | 13F20 11B65 13G05 |
本文献已被 ScienceDirect 等数据库收录! |
|