Arithmetic properties of periodic points of quadratic maps

Patrick Morton

Acta Arithmetica (1992)

  • Volume: 62, Issue: 4, page 343-372
  • ISSN: 0065-1036

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Patrick Morton. "Arithmetic properties of periodic points of quadratic maps." Acta Arithmetica 62.4 (1992): 343-372. <http://eudml.org/doc/206498>.

@article{PatrickMorton1992,
author = {Patrick Morton},
journal = {Acta Arithmetica},
keywords = {polynomial iteration; Galois group},
language = {eng},
number = {4},
pages = {343-372},
title = {Arithmetic properties of periodic points of quadratic maps},
url = {http://eudml.org/doc/206498},
volume = {62},
year = {1992},
}

TY - JOUR
AU - Patrick Morton
TI - Arithmetic properties of periodic points of quadratic maps
JO - Acta Arithmetica
PY - 1992
VL - 62
IS - 4
SP - 343
EP - 372
LA - eng
KW - polynomial iteration; Galois group
UR - http://eudml.org/doc/206498
ER -

References

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  1. [a] Modular Functions of One Variable IV, Lecture Notes in Math. 476, Springer, 1975. 
  2. [cm] A. R. Calderbank and P. Morton, Quasi-symmetric 3-designs and elliptic curves, SIAM J. Discrete Math. 3 (1990), 178-196. Zbl0742.05013
  3. [d] M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg 14 (1941), 197-272. Zbl0025.02003
  4. [fa] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366. 
  5. [fj] M. Fried and M. Jarden, Field Arithmetic, Ergeb. Math. Grenzgeb. 11, Springer, 1980. 
  6. [h1] H. Hasse, Zahlentheorie, Akademische Verlagsgesellschaft, Berlin 1969. 
  7. [h2] H. Hasse, Zur Theorie der abstrakten elliptischen Funktionenkörper I, II, III, J. Reine Angew. Math. 175 (1936), 55-62, 69-88, 193-208. 
  8. [h3] H. Hasse, Vorlesungen über Klassenkörpertheorie, Physica-Verlag, Würzburg 1967. Zbl0148.28005
  9. [m1] P. Morton and P. Patel, The Galois theory of periodic points of iterated polynomial maps, Wellesley College, 1992. Zbl0792.11043
  10. [m2] P. Morton, Periodic points of quadratic maps in characteristic 7, Wellesley College, 1992. 
  11. [m3] P. Morton, Characterizing cyclic cubic extensions by automorphism polynomials, J. Number Theory, to appear. Zbl0810.12003
  12. [n] W. Narkiewicz, Polynomial cycles in algebraic number fields, Colloq. Math. 58 (1989), 151-155. Zbl0703.12002
  13. [o1] R. W. K. Odoni, The Galois theory of iterates and composites of polynomials, Proc. London Math. Soc. 51 (1985), 385-414. Zbl0622.12011
  14. [o2] R. W. K. Odoni, Realising wreath products of cyclic groups as Galois groups, Mathematika 35 (1988), 101-113. Zbl0662.12010
  15. [pa] P. Patel, Topics in Computational Galois Theory, Honors thesis, Wellesley College, 1991. 
  16. [s] A. Schinzel, Selected Topics on Polynomials, University of Michigan Press, 1982. Zbl0487.12002
  17. [si] J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106, Springer, 1986. 
  18. [vh] F. Vivaldi and S. Hatjispyros, Galois theory of periodic orbits of rational maps, Nonlinearity 5 (1992), 961-978. Zbl0767.11049

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