Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves

TL;DR

This paper investigates the average behavior of Iwasawa invariants associated with Selmer groups of elliptic curves over anticyclotomic $ ext{Z}_p$-extensions, bridging arithmetic statistics and Iwasawa theory.

Contribution

It provides new insights into the statistical properties of Iwasawa invariants in anticyclotomic extensions, a topic less explored in existing literature.

Findings

Average Iwasawa invariants computed for elliptic curves over anticyclotomic extensions.

Results apply to both definite and indefinite cases.

Establishes connections between arithmetic statistics and Iwasawa theory.

Abstract

We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves, considered over anticyclotomic $\mathbb{Z}_p$-extensions in both the definite and indefinite settings. The results in this paper lie at the intersection of arithmetic statistics and Iwasawa theory.