Elliptic curves of high rank and the Riemann zeta function on the one\n line

2013/07/01 by Michael Rubinstein, Rubinstein, Michael O.
Mathematics · #11G05 #11M06 #11Y35 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1307.0420

openalex publication_date 2013/07/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We describe some experiments that show a connection between elliptic curves\nof high rank and the Riemann zeta function on the one line. We also discuss a\ncouple of statistics involving L-functions where the zeta function on the one\nline plays a prominent role.\n

Citations

• Zeros of principal L-functions and random matrix theory
• Modular Elliptic Curves and Fermat's Last Theorem

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• Zeta Functions for Elliptic Curves I. Counting Bundles
• Elliptic curves of unbounded rank and Chebyshev's bias
• Rank statistics for a family of elliptic curves over a function field
• The average analytic rank of elliptic curves
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