Arithmetic statistics and noncommutative Iwasawa theory
Copyright policy )Arithmetic statistics and noncommutative Iwasawa theory
Let p be an odd prime. Associated to a pair (E, \mathcal{F}_\infty) consisting of a rational elliptic curve E and a p -adic Lie extension \mathcal{F}_\infty of \mathbb{Q} , is the p -primary Selmer group \mathrm{Sel}_{p^{\infty}}(E/\mathcal{F}_\infty) of E over \mathcal{F}_\infty . In this paper, we study the arithmetic statistics for the algebraic structure of this Selmer group. The results provide insights into the asymptotics for the growth of Mordell-Weil ranks of elliptic curves in noncommutative towers.
Mathematics - Number Theory, arithmetic statistics, noncommutative Iwasawa theory, Akashi series, Selmer groups, growth of Mordell-Weil ranks, Elliptic curves over global fields, FOS: Mathematics, Euler characteristics, Number Theory (math.NT), 11R23, 11G05, Iwasawa theory
Mathematics - Number Theory, arithmetic statistics, noncommutative Iwasawa theory, Akashi series, Selmer groups, growth of Mordell-Weil ranks, Elliptic curves over global fields, FOS: Mathematics, Euler characteristics, Number Theory (math.NT), 11R23, 11G05, Iwasawa theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!