New York Journal of Mathematics
Volume 23 (2017) 1237-1264

  

Amir Akbary, Manoj Kumar, and Soroosh Yazdani

The signs in elliptic nets

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Published: September 18, 2017
Keywords: Elliptic divisibility sequences, division polynomials, elliptic nets, net polynomials
Subject: 11G05, 11G07, 11B37

Abstract
We give a generalization of a theorem of Silverman and Stephens regarding the signs in an elliptic divisibility sequence to the case of an elliptic net. We also describe applications of this theorem in the study of the distribution of the signs in elliptic nets and generating elliptic nets using the denominators of the linear combination of points on elliptic curves.

Acknowledgements

Research of the authors is partially supported by NSERC


Author information

Amir Akbary:
Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada
amir.akbary@uleth.ca

Manoj Kumar:
Pure Mathematics, University of Waterloo, 200 University Ave W, Waterloo, Ontario, N2L3G1, Canada
m29kumar@uwaterloo.ca

Soroosh Yazdani:
Pure Mathematics, University of Waterloo, 200 University Ave W, Waterloo, Ontario, N2L3G1, Canada
syazdani@gmail.com