Legendre polynomials and complex multiplication, I

JOURNAL OF NUMBER THEORY

卷:130

Article

Morton, Patrick¹ 

[1] Indiana Univ Purdue Univ, Dept Math, Indianapolis, IN 46202 USA

关键词: Legendre polynomial;    Class number;    Elliptic curve;    Multiplier;    Finite field;    Factorization;   

DOI  :  10.1016/j.jnt.2010.03.009

来源: Elsevier

【 摘 要 】

The factorization of the Legendre polynomial of degree (p - e)/4, where p is an odd prime, is studied over the finite field F(p.) It is shown that this factorization encodes information about the supersingular elliptic curves in Legendre normal form which admit the endomorphism root-2p, by 'proving an analogue of Deuring's theorem on supersingular curves with multiplier root-p. This is used to count the number of irreducible binomial quadratic factors of P((p-e)/4)(x) over F(p) in terms of the class number h(-2P). (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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