A NEW ASPECT OF CHEBYSHEV'S BIAS FOR ELLIPTIC CURVES OVER FUNCTION FIELDS

被引：1

作者：

Kaneko, Ikuya ^{[1
]}

Koyama, Shin-Ya ^{[2
]}

机构：

[1] CALTECH, Div Phys Math & Astron, 1200 E Calif Blvd, Pasadena, CA 91125 USA

[2] Toyo Univ, Dept Biomed Engn, 2100 Kujirai, Kawagoe, Saitama 3508585, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年

关键词：

Deep Riemann Hypothesis; Grand Riemann Hypothesis; Birch- Swinnerton-Dyer conjecture; L-functions; elliptic curves; function fields; Chebyshev bias;

D O I：

10.1090/proc/16461

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. This work addresses the prime number races for non-constant elliptic curves E over function fields. We prove that if rank(E) > 0, then there exist Chebyshev biases towards being negative, and otherwise there exist Chebyshev biases towards being positive. The key input is the convergence of the partial Euler product at the centre, which follows from the Deep Riemann Hypothesis over function fields.

引用

页码：5059 / 5068

页数：10

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