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Statistics for Iwasawa Invariants of elliptic curves, $\rm{II}$

Debanjana Kundu, Anwesh Ray

Abstract

We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves. These results lie at the intersection of arithmetic statistics and Iwasawa theory. We obtain unconditional lower bounds for the density of rational elliptic curves with prescribed Iwasawa invariants.

Statistics for Iwasawa Invariants of elliptic curves, $\rm{II}$

Abstract

We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves. These results lie at the intersection of arithmetic statistics and Iwasawa theory. We obtain unconditional lower bounds for the density of rational elliptic curves with prescribed Iwasawa invariants.

Paper Structure

This paper contains 7 sections, 23 theorems, 86 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Truncated Euler Characteristic
  4. Densities for Weierstrass Models of Elliptic curves
  5. The Euler characteristic on Average
  6. Iwasawa Invariants on Average
  7. Tables

Key Result

Lemma \oldthetheorem

The following inequality holds

Theorems & Definitions (48)

  • Conjecture \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • ...and 38 more