We give the maximal length of a Newton or a Schinzel sequence in a quadratic extension of a global field. In the case of a number field, the maximal length of a Schinzel sequence is 1, except in seven particular cases, and the Newton sequences are also finite, except for at most finitely many cases, all real. We give the maximal length of these sequences in the special cases. We have similar results in the case of a quadratic extension of a function field , taking in account that the ring of integers may be isomorphic to , in which case there are obviously infinite Newton and Schinzel sequences.
Keywords: Integer-valued polynomials, Newton and Schinzel sequences, Quadratic number and function fields
@article{ACIRM_2010__2_2_15_0,
author = {David Adam and Paul-Jean Cahen},
title = {Newton and {Schinzel} sequences in quadratic fields},
journal = {Actes des rencontres du CIRM},
pages = {15--20},
publisher = {CIRM},
volume = {2},
number = {2},
year = {2010},
doi = {10.5802/acirm.28},
zbl = {06938576},
language = {en},
url = {https://pmb.cedram.org/articles/10.5802/acirm.28/}
}
TY - JOUR AU - David Adam AU - Paul-Jean Cahen TI - Newton and Schinzel sequences in quadratic fields JO - Actes des rencontres du CIRM PY - 2010 SP - 15 EP - 20 VL - 2 IS - 2 PB - CIRM UR - https://pmb.cedram.org/articles/10.5802/acirm.28/ DO - 10.5802/acirm.28 LA - en ID - ACIRM_2010__2_2_15_0 ER -
David Adam; Paul-Jean Cahen. Newton and Schinzel sequences in quadratic fields. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 15-20. doi : 10.5802/acirm.28. https://pmb.cedram.org/articles/10.5802/acirm.28/
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