Mahler's measure and elliptic curves with potential complex multiplication

2020/05/08 by Pengo, Riccardo
#11R06 #11S40 #14K22 #19F27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.04159

Abstract

Given an elliptic curve E defined over ℚ which has potential complex multiplication by the ring of integers O_K of an imaginary quadratic field K we construct a polynomial P_E ∈ ℤ[x,y] which is a planar model of E and such that the Mahler measure m(P_E) ∈ ℝ is related to the special value of the L-function L(E,s) at s = 2.

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