caa a22 4500 60552579X CHVBK 20210128100800.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10958-015-2531-1 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2531-1 Polynomial Interpolation over the Residue Rings Z n [Elektronische Daten] [N. Vasiliev, O. Kanzheleva] We consider the problem of polynomial interpolation over the residue rings Z n . The general case can easily be reduced to the case of n = p k due to the Chinese reminder theorem. In contrast to the interpolation problem over fields, the case of rings is much more complicated due to the existence of nonzero polynomials representing the zero function. Also, the result of interpolation is not unique in the general case. We compute, using the CAS system Singular, Gröbner bases of the ideals of null polynomials over residue rings. This allows us to obtain a canonical form for the results of interpolation. We also describe a connection between estimates on the cardinality of interpolating sets and estimates on the total number of permutation polynomials over the residue ring. In particular, we give a recurrence formula for the number of permutation polynomials over Z p k . Springer Science+Business Media New York, 2015 Vasiliev N. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia aut Kanzheleva O. Google Corporation, Irvine, USA aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 845-850 1072-3374 209:6<845 2015 209 10958 https://doi.org/10.1007/s10958-015-2531-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2531-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Vasiliev N. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia aut NATIONALLICENCE 700 1- Kanzheleva O. Google Corporation, Irvine, USA aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 845-850 1072-3374 209:6<845 2015 209 10958