Elliptic fibrations and $3 \cdot 2^k$

TL;DR

This paper investigates the statistical properties of elliptic fibrations and class groups of quadratic fields, providing bounds on exponential moments of their ranks and torsion elements.

Contribution

It establishes the order of magnitude for exponential moments of the rank in elliptic fibrations and for the 3·2^k torsion in quadratic class groups, a novel quantitative analysis.

Findings

Bounds on exponential moments of elliptic fibration ranks

Order of magnitude for 3·2^k torsion in class groups

Quantitative understanding of these algebraic structures

Abstract

We determine the order of magnitude for all exponential moments of the rank in a broad class of elliptic fibrations and for the $3 \cdot 2^k$-torsion in the class group of quadratic fields.