bio | website | perso.ens-lyon.fr/… |
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location | Lyon | |
age | 34 | |
visits | member for | 3 years, 10 months |
seen | Nov 10 '13 at 12:21 | |
stats | profile views | 2,299 |
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 |