Arithmetic properties of periodic points of quadratic maps

• Autorzy: Patrick Morton
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 62
• Numer: 4
• Strony: 343-372

Daty

wydano

1992

otrzymano

1991-09-13

Twórcy

autor

Patrick Morton

• Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02181, U.S.A.

Bibliografia

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