ON THE RANKS OF THE JACOBIANS OF CURVES DEFINED BY JACOBI POLYNOMIALS

JOHN CULLINAN; ANASTASSIA ETROPOLSKI; ELIZABETH SELL

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ON THE RANKS OF THE JACOBIANS OF CURVES DEFINED BY JACOBI POLYNOMIALS

机译：关于雅各比多项式定义的曲线的雅各比的级数

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We show that the degree-3 Jacobi Polynomials define two one-parameter families of elliptic curves E_r/Q(r) and F_s/Q(s) with positive rank outside of an explicit finite set of (r, s) ∈ Q × Q. In addition we initiate a program to study the ranks of the Jacobians of these curves in higher degree.

机译：我们显示3级Jacobi多项式定义了两个单参数椭圆曲线族E_r / Q（r）和F_s / Q（s），它们的正秩在（r，s）∈Q×Q的显式有限集之外此外，我们启动了一个程序，以更高程度研究这些曲线的雅可比行列。

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《The Rocky Mountain journal of mathematics》 |2014年第1期|共11页
作者
JOHN CULLINAN; ANASTASSIA ETROPOLSKI; ELIZABETH SELL;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
RANKS; JACOBIANS; CURVES;

机译：排名;雅各布;曲线;

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1. 雅各比级数所定义整函数的极大项 [J] . 王安斌数学季刊：英文版 . 1989,第004期
2. ON THE RANKS OF THE JACOBIANS OF CURVES DEFINED BY JACOBI POLYNOMIALS [J] . JOHN CULLINAN, ANASTASSIA ETROPOLSKI, ELIZABETH SELL The Rocky Mountain journal of mathematics . 2014,第1期

机译：关于雅各比多项式定义的曲线的雅各比的级数
3. The p-rank of the reduction mod p of Jacobians and Jacobi sums [J] . A. Alvarez International Journal of Number Theory . 2014,第8期

机译：Jacobian和Jacobi和的归约模p的p秩
4. Jacobi inversion on strata of the Jacobian of the C_(rs) curve y~r = f(x), Ⅱ [J] . Shigeki Matsutani, Emma Previato Journal of the Mathematical Society of Japan . 2014,第2期

机译：C_（rs）曲线y〜r = f（x），Ⅱ的雅可比行列上的Jacobi反演
5. Characteristic Polynomials of a Class of Jacobi Quartic Curves over Finite Field [C] . Dongqin Wang, Lin You International Conference on Mathematics and Computers in Sciences and in Industry . 2014

机译：有限域上一类Jacobi四次曲线的特征多项式
6. The projective geometry of curves of genus one, and an algorithm for the Jacobian of such a curve [D] . Perlis, Alexander R. 2004

机译：一类曲线的射影几何以及这种曲线的雅可比算术
7. Representation of ... formula ...-Bernstein polynomials in terms of ... formula ...-Jacobi polynomials [O] . F Soleyman, I Area, M Masjed-Jamei, -1

机译：... ... ...-Bernstein多项式的表示形式... ... ... -Jacobi多项式
8. JACOBI SUMS, FERMAT JACOBIANS, AND RANKS OF ABELIAN VARIETIES OVER TOWERS OF FUNCTION FIELDS [O] . Douglas Ulmer 2006

机译：JaCOBI sUms，FERmaT JaCOBIaNs，以及功能领域的aBELIaN品种等级
9. Jacobi Polynomials as Generalized Faber Polynomials [R] . Zayed, A. I. 1987

机译：Jacobi多项式作为广义Faber多项式

ON THE RANKS OF THE JACOBIANS OF CURVES DEFINED BY JACOBI POLYNOMIALS

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