Statistics for Iwasawa invariants of elliptic curves

Abstract

We study the average behaviour of the Iwasawa invariants for the Selmer groups of elliptic curves, setting out new directions in arithmetic statistics and Iwasawa theory.

arXiv commentFinal version, to appear in Transactions of the AMS. 18 pages

References in corpus (5)

• Iwasawa Main Conjecture for Supersingular Elliptic Curves and BSD conjecture
• Euler Characteristics and their Congruences for Multi-signed Selmer Groups
• Anomalous Primes and the Elliptic Korselt Criterion
• Counting elliptic curves with bad reduction over a prescribed set of primes
• Families of elliptic curves ordered by conductor

Cited by in corpus (7)

• Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves
• Arithmetic statistics and diophantine stability for elliptic curves
• Asymptotic growth of Mordell-Weil ranks of elliptic curves in noncommutative towers
• Rank Jumps and Growth of Shafarevich--Tate Groups for Elliptic Curves in $\mathbb{Z}/p\mathbb{Z}$-Extensions
• Remarks on Hilbert's tenth problem and the Iwasawa theory of elliptic curves
• Arithmetic statistics for the Fine Selmer group in Iwasawa theory
• Statistics for Iwasawa Invariants of elliptic curves, $\mathrm{II}$