Elliptic Curve Groups and Chip-Firing Games
نویسنده
چکیده
Abstract. The author illustrates several results from the theory of elliptic curves, as well as the theory of chip-firing games on graphs. More specifically, in both of these cases, we obtain analogues of cyclotomic polynomials with several combinatorial and number theoretic properties. We also provide an analysis of zeta functions which highlights the connections between these two disparate fields.
منابع مشابه
Combinatorial Aspects of Elliptic Curves Ii: Relationship between Elliptic Curves and Chip-firing Games on Graphs
Let q be a power of a prime and E be an elliptic curve defined over Fq. In [17], the present author examined a sequence of polynomials which express the Nk’s, the number of points on E over the field extensions Fqk , in terms of the parameters q and N1 = #E(Fq). These polynomials have integral coefficients which alternate in sign, and a combinatorial interpretation in terms of spanning trees of...
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تاریخ انتشار 2007