Florian Breuer

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20232025

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5 papers · 1 filter

math.NT2025

Partitions and Hecke images

Florian Breuer, Fabien Pazuki

We obtain a new family of relations satisfied by the partition function. In contrast with most partition relations, these involve non-trivial roots of unity. We present two proofs,…

math.NT2025

Divisibility of the coefficients of modular polynomials

Florian Breuer

Let $N > 1$ and let $Φ_{N} (X, Y) \in Z [X, Y]$ be the modular polynomial which vanishes precisely at pairs of $j$ -invariants of elliptic curves linked by a cyclic isogeny of degree…

math.NT2024

Drinfeld modular polynomials of level $T$

Florian Breuer, Mahefason Heriniaina Razafinjatovo

We investigate Drinfeld modular polynomials parametrizing $T$ -isogenies between Drinfeld $F_{q} [T]$ -modules of rank $r \geq 2$ . By providing an explicit classification of suc…

math.NT2024

Heights of Drinfeld modular polynomials and Hecke images

Florian Breuer, Fabien Pazuki, Zhenlin Ran

We obtain explicit upper and lower bounds on the size of the coefficients of the Drinfeld modular polynomials $Φ_{N}$ for any monic $N \in F_{q} [t]$ . These polynomials vanish at…

math.NT2023

Explicit bounds on the coefficients of the modular polynomials and the size of $X_{0} (N)$

Florian Breuer, Desirée Gijón Gómez, Fabien Pazuki

We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials $Φ_{N}$ for the elliptic $j$ -function. These bounds make explicit the best previous…