Some remarks on the Picard curves over a finite field | Zendy

Takizawa Yoh | Zendy

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Some remarks on the Picard curves over a finite field

Author(s) -

Takizawa Yoh

Publication year - 2007

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410515

Subject(s) - mathematics , newton polygon , polygon (computer graphics) , finite field , field (mathematics) , polynomial , pure mathematics , combinatorics , mathematical analysis , telecommunications , frame (networking) , computer science

In this paper we study the Newton polygon of the L ‐polynomial L ( t ) associate to the Picard curves y 3 = x 4 – 1, y 3 = x 4 – x defined over a finite field p . In the former case we get a complete classification. In the latter case we obtained a partial result. As a consequence of our result we obtain a criterion to find a supersingular Picard curves for the above two cases. Our main results are stated in Theorems 3.1 and 4.1. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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