Polynomial cycles in certain rings of rationals
Journal de théorie des nombres de Bordeaux (2002)
- Volume: 14, Issue: 2, page 529-552
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topNarkiewicz, Władysław. "Polynomial cycles in certain rings of rationals." Journal de théorie des nombres de Bordeaux 14.2 (2002): 529-552. <http://eudml.org/doc/248910>.
@article{Narkiewicz2002,
abstract = {It is shown that the methods established in [HKN3] can be effectively used to study polynomial cycles in certain rings. We shall consider the rings $\mathbf \{Z\} [\frac\{1\}\{N\}]$ and shall describe polynomial cycles in the case when $N$ is either odd or twice a prime.},
author = {Narkiewicz, Władysław},
journal = {Journal de théorie des nombres de Bordeaux},
language = {eng},
number = {2},
pages = {529-552},
publisher = {Université Bordeaux I},
title = {Polynomial cycles in certain rings of rationals},
url = {http://eudml.org/doc/248910},
volume = {14},
year = {2002},
}
TY - JOUR
AU - Narkiewicz, Władysław
TI - Polynomial cycles in certain rings of rationals
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 2
SP - 529
EP - 552
AB - It is shown that the methods established in [HKN3] can be effectively used to study polynomial cycles in certain rings. We shall consider the rings $\mathbf {Z} [\frac{1}{N}]$ and shall describe polynomial cycles in the case when $N$ is either odd or twice a prime.
LA - eng
UR - http://eudml.org/doc/248910
ER -
References
top- [A1] L.J. Alex, Diophantine equations related to finite groups. Comm. Algebra4 (1976), 77-100. Zbl0324.20010MR424675
- [A2] L.J. Alex, On the diophantine equation 1 + 2α = 3b5c + 2d3e5f. Math. Comp.44 (1985), 267-278.
- [AF1] L.J. Alex, L.L. Foster, On the diophantine equation 1 + pa =2b + 2cpd. Rocky Mount. J. Math.15 (1985), 739-761. Zbl0589.10017MR813272
- [AF2] L.J. Alex, L.L. Foster, On the diophantine equation 1 + x + y = z. Rocky Mount. J. Math.22 (1992), 11-62. Zbl0760.11013MR1159941
- [Ba] C. Batut, D. Bernardi, H. Cohen, M. Olivier, User's Guide to PARI-GP, Bordeaux1994.
- [Ca] J.W.S. Cassels, On the equation ax - by = 1. Amer. J. Math.75 (1953), 159-162. Zbl0050.03703MR51851
- [Co] J.H.E. Cohn, The Diophantine equation x2 + 3 = yn. Glasgow Math. J.35 (1993), 203-206. Zbl0779.11015MR1220562
- [Da] M. Daberkow, C. Fieker, J. Kluners, M. Pohst, K. Roegner, M. Schornig, K. Wildanger, Kant V4. J. Symbolic Comput. 24 (1997), 267-283. Zbl0886.11070MR1484479
- [HKN1] F. Halter-Koch, W. Narkiewicz, Polynomial cycles in finitely generated domains. Monatsh. Math.119 (1995), 275-279. Zbl0840.13003MR1328818
- [HKN2] F. Halter-Koch, W. Narkiewicz, Polynomial cycles and dynamical units. Proc. Conf. Analytic and Elementary Number Theory, 70-80, Wien, 1996. Zbl0882.12003
- [HKN3] F. Halter-Koch, W. Narkiewicz, Scarcity of finite polynomial orbits. Publ. Math. Debrecen56 (2000), 405-414. Zbl0961.11005MR1765989
- [Le] D.H. Lehmer, On a problem of Störmer. Illinois J. Math.8 (1964), 57-79. Zbl0124.27202MR158849
- [Len] H.W. LenstraJr., Euclidean number fields of large degree. Invent. Math.38 (1977), 237-254. Zbl0328.12007MR429826
- [LN] A. Leutbecher, G. Niklasch, On cliques of exceptional units and Lenstra's construction of Euclidean fields. Number Theory, Lecture Notes in Math.1380, 150-178, Springer, 1989. Zbl0703.11056MR1009799
- [MDT] D Z. Mo, R.TIJDEMAN, Exponential diophantine equations with four terms. Indag. Math.(N.S.) 3 (1992), 47-57. Zbl0765.11018MR1157518
- [Mo] P. Morton, Arithmetic properties of periodic points of quadratic maps, II. Acta Arith.87 (1998), 89-102. Zbl1029.12002MR1665198
- [N1] W. Narkiewicz, Polynomial Mappings. Lecture Notes in Math.1600, Springer, 1995. Zbl0829.11002MR1367962
- [NP] W. Narkiewicz, T. Pezda, Finite polynomial orbits in finitely generated domains. Monatsh. Math.124 (1997), 309-316. Zbl0897.13024MR1480362
- [Pe] T. Pezda, Polynomial cycles in certain local domains. Acta Arith.66 (1994), 11-22. Zbl0803.11063MR1262650
- [Pi] S.S. Pillai, On the equation 2x - 3y = 2X + 3Y. Bull. Calcutta Math. Soc.37 (1945), 15-20. Zbl0063.06245
- [Sch] H.P. Schlickewei, S-units equations over number fields. Invent. Math.102 (1990), 95-107. Zbl0711.11017MR1069241
- [Sc] R. Scott, On the equation px - by = c and ax + by = cz. J. Number Theory44 (1993), 153-165. Zbl0786.11020MR1225949
- [Si] W. Sierpinski, Sur une question concernant le nombre de diviseurs premiers d'un nombre naturel. Colloq. Math.6 (1958), 209-210. Zbl0086.03503MR104621
- [Sk] C.M. Skinner, On the diophantine equation apx +bqy = c + dpz qw. J. Number Theory35 (1990), 194-207. Zbl0703.11017MR1057322
- [St] C. Störmer, Quelques théorèmes sur l'équation de Pell x2 - Dy2 = ±1 et leurs applications. Skr. Vidensk.-selsk. (Christiania) I, Mat. Naturv. Kl. (1897), no.2, 1-48.
- [TW] R. Tijdeman, L. Wang, Sums of products of powers of given prime numbers. Pacific J. Math.132 (1988), 177-193; corr. ibidem135 (1988), 396-398. Zbl0606.10012MR929588
- [Wa] C.T.C. Wall, A theorem on prime powers. Eureka19 (1957), 10-11. MR83499
- [Wg] L.X. Wang, Four terms equations. Indag. Math.51 (1989), 355-361. Zbl0698.10011MR1020029
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.