F. Brunault

activity

20122026

K_{4}

group of modular curves

2 citations · 2 across the 8 of their papers we have counts for

collaborators

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8 papers · 1 filter

math.NT2026

Bernoulli determinants and cuspidal subgroups

François Brunault

We give an explicit formula for the order of the rational cuspidal class group of the modular curve $X_{1} (N)$ for an arbitrary integer $N$ . The proof relies on results of Streng on…

math.NT2026

Elements in $K_{4}$ and regulator maps of Fermat curves

François Brunault, David T. -B. G. Lilienfeldt, Yusuke Nemoto

We construct explicit elements in the group $K_{4}^{(3)}$ of the Fermat curves $x^{N} + y^{N} = 1$ for all $N \geq 3$ . The construction, which is uniform in $N$ , uses polylogarithmic complexe…

math.NT2024

$K_{2}$ of families of elliptic curves over non-Abelian cubic and quartic fields

François Brunault, Rob de Jeu, Hang Liu +1

We give two constructions of families of elliptic curves over cubic or quartic fields with three, respectively four, `integral' elements in the kernel of the tame symbol on the cur…

math.NT2023

On the Mahler measure of $(1 + x) (1 + y) + z$

François Brunault

We prove a conjecture of Boyd and Rodriguez Villegas relating the Mahler measure of the polynomial $(1 + x) (1 + y) + z$ and the value at $s = 3$ of the $L$ -function of an elliptic curve of…

math.NT2020★ 2 cited

On the $K_{4}$ group of modular curves

François Brunault

We construct elements in the $K_{4}$ group of modular curves using the polylogarithmic complexes of weight 3 defined by Goncharov and De Jeu. The construction is uniform in the level…

math.NT2019

Note on Fourier expansions at cusps

François Brunault, Michael Neururer

This was originally an appendix to our paper `Fourier expansions at cusps' [arXiv:1807.00391]. The purpose of this note is to give a proof of a theorem of Shimura on the action of…

math.NT2017

On the modularity of endomorphism algebras

François Brunault

We use the adelic language to show that any homomorphism between Jacobians of modular curves arises from a linear combination of Hecke modular correspondences. The proof is based o…

math.NT2012

On Zagier's conjecture for base extensions of elliptic curves

François Brunault

Let E be an elliptic curve over Q, and let F be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjectu…

Bernoulli determinants and cuspidal subgroups

Elements in K4​ and regulator maps of Fermat curves

K2​ of families of elliptic curves over non-Abelian cubic and quartic fields

On the Mahler measure of (1+x)(1+y)+z

On the K4​ group of modular curves

Note on Fourier expansions at cusps

On the modularity of endomorphism algebras

On Zagier's conjecture for base extensions of elliptic curves

Elements in $K_{4}$ and regulator maps of Fermat curves

$K_{2}$ of families of elliptic curves over non-Abelian cubic and quartic fields

On the Mahler measure of $(1 + x) (1 + y) + z$

On the $K_{4}$ group of modular curves