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Moments of quadratic twists of elliptic curve L-functions over function fields
Algebra & Number Theory ( IF 1.3 ) Pub Date : 2020-08-18 , DOI: 10.2140/ant.2020.14.1853
Hung M. Bui , Alexandra Florea , Jonathan P. Keating , Edva Roditty-Gershon

We calculate the first and second moments of L-functions in the family of quadratic twists of a fixed elliptic curve E over F_q[x], asymptotically in the limit as the degree of the twists tends to infinity. We also compute moments involving derivatives of L-functions over quadratic twists, enabling us to deduce lower bounds on the correlations between the analytic ranks of the twists of two distinct curves.

中文翻译:

椭圆曲线 L 函数在函数域上的二次扭曲矩

我们在 F_q[x] 上的固定椭圆曲线 E 的二次扭曲族中计算 L 函数的一阶和二阶矩,随着扭曲的程度趋于无穷,渐近地处于极限。我们还计算涉及二次扭曲的 L 函数导数的矩,使我们能够推导出两条不同曲线的扭曲的分析等级之间的相关性的下限。
更新日期:2020-08-18
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