Moscow Mathematical Journal

Volume 15, Issue 1, January–March 2015 pp. 89–100.

A Proof of a Conjecture by Lӧtter on the Roots of a Supersingular Polynomial and its Application

Authors: Takehiro Hasegawa
Author institution:Faculty of Education, Shiga University, Otsu, Shiga 520-0862, Japan

Summary:

In this paper, we prove a conjecture by E. C. Lӧtter on the roots of a supersingular polynomial. As its application, we present two optimal towers over finite fields corresponding to the sequences of elliptic modular curves X₀(3 · 2ⁿ⁺²) and X₀(2 · 3ⁿ⁺²).

2010 Math. Subj. Class. 11R58, (11G20, 14G15).

Keywords: Finite fields, recursive towers of function fields, generating function of the franel number.

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