ON THE ZETA FUNCTION AND THE AUTOMORPHISM GROUP OF THE GENERALIZED SUZUKI CURVE

Author(s)

Borges, Herivelto ^[1] ; Coutinho, Mariana ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

^[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 374, n. 3, p. 1899-1917, MAR 2021.
• Web of Science Citations: 0

Abstract

For p an odd prime number, q(o) = p(t), and q = p(2t-1), let chi(gs) be the nonsingular model of Y-q - Y = X-qo (X-q - X). In the present work, the number of F(q)n-rational points and the full automorphism group of chi(gs) are determined. In addition, the L-polynomial of this curve is provided, and the number of F(q)n,-rational points on the Jacobian J(chi gs) is used to construct etale covers of chi(gs), some with many rational points. (AU)

• FAPESP's process: 18/23839-0 - Algebraic Curves over Finite Fields
• Grantee: Mariana de Almeida Nery Coutinho
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 17/04681-3 - Algebraic curves over finite fields
• Grantee: Herivelto Martins Borges Filho
• Support Opportunities: Regular Research Grants