François Brunault

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7,510 reputation
11741
bio website perso.ens-lyon.fr/…
location Lyon
age 34
visits member for 3 years, 10 months
seen Nov 10 '13 at 12:21

I am a number theorist working at the École normale supérieure de Lyon in France. My research interests are elliptic curves, L-functions and zeta functions, especially the study of their special values (conjectures by Beilinson, Bloch, Kato, Zagier...).


Mar
18
awarded  Notable Question
Nov
23
awarded  Nice Answer
Nov
11
awarded  Good Answer
Nov
10
revised calculate function from its divizor
Updated link
Oct
31
comment calculate function from its divizor
Dear Hicham, I edited my answer to give the link to the Pari/GP script.
Oct
31
revised calculate function from its divizor
Added link to Pari/GP script.
Jun
25
awarded  ag.algebraic-geometry
Jun
25
awarded  nt.number-theory
Jun
25
awarded  Revival
Jun
25
awarded  Pundit
Jun
24
answered On Deligne's determinant of motives
Jun
19
comment modularity of elliptic curves with cm
Note that if $\operatorname{Res}_{F/\mathbf{Q}} E$ appear inside $J_1(N)$ over $\mathbf{Q}$ then $E$ itself appears inside $J_1(N)$ over $F$. So in this case you can find a modular parametrization $X_1(N) \to E$ which is defined over $F$.
Jun
19
comment modularity of elliptic curves with cm
What is true is that every elliptic curve over $\overline{\mathbf{Q}}$ with CM by $K$ is isomorphic over $\overline{\mathbf{Q}}$ to a $K$-curve (a curve which is isogenous over $\overline{\mathbf{Q}}$ to all its $\operatorname{Gal}(\overline{\mathbf{Q}}/K)$-conjugates), see Wortmann's article and the references.
Jun
19
comment modularity of elliptic curves with cm
In the last sentence, I meant "isomorphic over $\overline{\mathbf{Q}}$"...
Jun
19
comment modularity of elliptic curves with cm
There is a nice article where Shimura's result is generalized for a wider class of CM elliptic curves, see S. Wortmann, *Generalized Q-curves and factors of $J_1(N)$* dx.doi.org/10.1007/BF02940901 These CM elliptic curves are sometimes called of Shimura type. I'm not sure but I think these are exactly the CM elliptic curves whose restriction of scalars appear inside $J_1(N)$ over $\mathbf{Q}$. Moreover, every CM elliptic curve is isomorphic over $\mathbf{Q}$ to a curve of Shimura type.
Jun
15
comment Mersenne Prime Sequences
@Dietrich : Eugène Catalan's footnote is here archive.org/stream/nouvellecorresp01mansgoog#page/n353/mode/2up In fact, he states this as an "empirical theorem" which holds for all terms "up to a certain limit". To me this seems far from conjecturing that all terms are prime.
Jun
15
comment Mersenne Prime Sequences
@Barakman : The point is that there is no obvious bias towards primality arising from belonging to $A_n$. The exponents of the numbers in $A_n$ are very large, and I see no reason why they should be more prime than the Mersenne numbers of comparable size. So their primality becomes soon unlikely.
Jun
15
comment Mersenne Prime Sequences
The Wagstaff heuristics primes.utm.edu/mersenne/heuristic.html assert that for large prime $p$, the probability of $2^p-1$ being prime is about $(\log p)/p$ (up to some multiplicative constant). So it seems unlike to me that $A_n$ contains only prime numbers. I would rather conjecture that any such sequence will contain a composite number.
Jun
15
comment How to explain the picturesque patterns in François Brunault's matrix?
Thank you for spotting these nice patterns! Not a precise explanation, but it may not be surprising that the entries of the matrix have nice $p$-adic properties. Indeed, any generalized polynomial map (in the sense of the question you link to) extends to a map $\mathbf{Z}_p \to \mathbf{Z}_p$ which is continuous (and in fact, 1-Lipschitz).
Jun
15
comment Elementary tools for proving congruences of modular forms
See E. Ghate, An introduction to congruences between modular forms math.tifr.res.in/%7Eeghate/basics.dvi