ON THE NON-VANISHING OF ELLIPTIC CURVE L-FUNCTIONS AT THE CENTRAL POINT

2004/12/31 by Matthew P. Young
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Distribution (mathematics) #Elliptic curve #Elliptic function #Geometry #Mathematical analysis #Mathematics #Point (geometry) #Pure mathematics #Riemann hypothesis #Riemann surface #math.NT

paper · pdf · doi:10.1017/s0024611506015760

published as Proc. London Math. Soc. (3) 93 (2006), no. 1, 1-42 · 38 pages. v3: Improved and expanded exposition, error corrections. To appear in the Proceedings of the London Mathematical Society

arxiv created 2005/10/24 · openalex publication_date 2006/06/09 · arxiv updated 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that a large number of elliptic curve L-functions do not vanish at the central point, conditionally on the Generalized Riemann Hypothesis and on an assumption on the regular distribution of the root number.

Citations

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