Florian Breuer

Wednesday, 15 February 2023
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.
Florian Breuer
Number Theory
University of Newcastle
Wednesday 15 February 2023, 3pm
RC-4082