Bounded ranks and Diophantine error terms

2018/05/29 by Hector Pasten, Pasten, Hector · 2 citations
Mathematics · #11J97 #FOS: Mathematics #Number Theory (math.NT) #Primary 11G05 #Secondary 11J25 #math.NT #msc:11G05 #msc:11J25 #msc:11J97

paper · pdf · doi:10.48550/arxiv.1805.11205

arxiv created 2018/06/29 · arxiv updated 2018/07/03

Abstract

We show that Lang's conjecture on error terms in Diophantine approximation implies Honda's conjecture on ranks of elliptic curves over number fields. We also show that even a very weak version of Lang's error term conjecture would be enough to deduce boundedness of ranks for quadratic twists of elliptic curves over number fields. This can be seen as evidence for boundedness of ranks not relying on probabilistic heuristics on elliptic curves.

Cited by

• Rank of Jacobian Varieties of Curves y^s=x(ax^r+b)
• On the Rank of Jacobian Varieties of the Curves y^s=ax^r+b

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