Height Functions for Groups of S-units of Number Fields and Reductions Modulo Prime Ideals

• Autorzy: Barańczuk S.

Identyfikatory

DOI

10.4064/ba63-1-4

• Języki publikacji: EN

Abstrakty

EN

A result on the orders of the reductions of an element of the group of S-units of a number field is obtained by investigating three height functions for groups of S-units of number fields which are analogous to local, global and canonical height functions for elliptic curves.

Słowa kluczowe

EN

S-units; reductions; height functions; primitive divisors

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: Vol. 63, no. 1
• Strony: 25--31
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Barańczuk S.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland

Bibliografia

• [BG] E. Bombieri and W. Gubler, Heights in Diophantine Geometry, Cambridge Univ. Press, 2006.
• [ChH] J. Cheon and S. Hahn, The orders of the reductions of a point in the Mordell–Weil group of an elliptic curve, Acta Arith. 88 (1999), 219–222.
• [L] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983.
• [Sch] A. Schinzel, Primitive divisors of the expression An - Bn in algebraic number fields, J. Reine Angew. Math. 268 (1974), 27–33.
• [Si1] J. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986.
• [Si2] J. Silverman, Wieferich’s criterion and the abc-conjecture, J. Number Theory 30 (1988), 226–237.
• [Zim] H. G. Zimmer, On the difference of the Weil height and the Néron–Tate height, Math. Z. 147 (1976), 35–51.