Wednesday, 15 February 2023

### Abstract

Consider the classical modular $j$-function on the upper half-plane, and let $N$ be a positive integer. Then the modular polynomial $\Phi_N(X,j)$ is the minimal polynomial of $j(N\tau)$ over the field of modular functions $\mathbb{C}(j(\tau))$.

These polynomials, which are used in certain cryptosystems, have integer coefficients which are surprisingly large, yet many algorithms for computing them require an explicit upper bound on these coefficients.

I will outline joint work with Fabien Pazuki obtaining an explicit upper bound on the size of these coefficients.

Speaker

Florian Breuer

Research area

Number Theory

Affilation

University of Newcastle

Date

Wednesday 15 February 2023, 3pm

Location

RC-4082