Computing the average root number of an elliptic surface

DOI10.1016/j.jnt.2018.07.012zbMath1476.11088arXiv1801.02283OpenAlexW2963854724MaRDI QIDQ1788091

Jake Chinis

Publication date: 8 October 2018

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.02283

zbMATH Keywords

rankroot numberaverage root number

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (2)

Root number in Integer parameter families of elliptic curves ⋮ Constant root number on integer fibres of elliptic surfaces

Uses Software

• PARI/GP

Cites Work

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• Calculating root numbers of elliptic curves over \(\mathbb{Q}\)
• Non-isotrivial elliptic surfaces with non-zero average root number
• Modular elliptic curves and Fermat's Last Theorem
• Root numbers and ranks in positive characteristic
• A GENERALIZATION OF THE CONGRUENT NUMBER PROBLEM
• Class Numbers of the Simplest Cubic Fields
• Signes locaux des courbes elliptiques en 2 et 3
• Heights and the specialization map for families of abelian varieties.
• On the square-free sieve
• One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries

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