8,063 reputation
12050
bio website perso.ens-lyon.fr/…
location Lyon
age 36
visits member for 5 years, 3 months
seen yesterday

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...).


Jul
19
comment Field of definition of dominant morphisms
@Will, thanks for the clarification.
Jul
19
comment Field of definition of dominant morphisms
@Will "Each point defines a morphism" do you mean each point of Spec of your algebra over $k_0$?
Jul
13
comment Can one define “Ramanujan Summation” over algebraic number fields?
In the case K=Q, the sum of the norms of the ideals boils down exactly to the sum over positive integers.
Jul
13
comment Can one define “Ramanujan Summation” over algebraic number fields?
Your sum looks like the L-function of a Grössencharakter of $\mathbf{Z}[i]$ evaluated at $s=0$ (but I'm unsure of the details).
Jul
13
comment Can one define “Ramanujan Summation” over algebraic number fields?
It seems john mangual doesn't want to sum the norms of the ideals of $\mathbf{Z}[i]$, but he would like to sum the generators of these ideals (say in the first quadrant).
Jul
2
comment Is it possible to evaluate Connect 4 positions with Combinatorial Game Theory?
If I recall correctly, Connect 4 is a first player win.
Jul
2
comment Is it possible to evaluate Connect 4 positions with Combinatorial Game Theory?
Just for the record, Connect 4 has already been solved around 1988 tromp.github.io/c4/c4.html
Jun
27
comment Computing an eigencuspform in $S_2(\Gamma_0(1776))$
The natural way to embed abelian varieties into projective space is to use theta functions. Then, finding equations amounts to find algebraic relations between them. The first theta relations were found by Riemann, they are quadratic. Moreover, by results of Mumford and Kempf, if the line bundle is ample enough then Riemann's relations generate all the relations. For an abelian 3-fold, the best you can hope for is embedd into $\mathbf{P}^7$, but if you want quadratic equations you probably need higher dimensional projective space. See Chap. 7 in Birkenhake-Lange "Complex abelian varieties".
Jun
26
comment Computing an eigencuspform in $S_2(\Gamma_0(1776))$
For your second question, as you probably know there is no such thing as Cremona's tables for abelian varieties. On the other hand, you can try to compute the complex periods of $A_f$ (using modular symbols). At least they determine $A_f$ as an abelian variety over C, but then it depends on what you want to do.
Jun
19
comment different definitions of epsilon constants for representations of GL(2) from modular forms
You can also look at Gealy's thesis thesis.library.caltech.edu/5020 where he recalls the normalization for the global L-function and epsilon-factor of a modular form (see Section 5.4 but also Chapter 8 for the finite epsilon factors). In any case, I think it's reasonable to ask that the epsilon factor should be 1 whenever the representation is unramified (in GL(1) as well as GL(2) case).
Jun
2
awarded  Yearling
May
15
comment On a result attributed to W. Ljunggren and T. Nagell
According to the Zentralblatt review of Ljunggren's article, the method is to reduce to a (Pell-)Fermat equation. zbmath.org/?q=an:0028.00901
May
10
awarded  Nice Question
May
9
comment Elliptic curves and supercuspidal representations of conductor $p^2$
Thanks David, I'm indeed using your algorithm to compute the examples in my comment to @GuestPoster above. I will see if I can find more patterns.
May
9
comment Elliptic curves and supercuspidal representations of conductor $p^2$
@GuestPoster I've written a Magma code and for $p=11$ it seems to be the case that $\phi$ has order 6, 4, 3, 3 according to whether $v_p(\Delta)$ is 2, 3, 4, 8, so your guess seems right. For $p=5$ I have examples where $(v_p(\Delta),\textrm{ord}(\phi))=(2,3),(2,6),(4,3),(4,6),(8,3),(8,6)$ so $v_p(\Delta)$ seems not sufficient to determine $\phi$. For $p=17$ I have a $(2,3)$-example. If you could elaborate on your comment, this would make a nice answer!
May
8
comment Elliptic curves and supercuspidal representations of conductor $p^2$
Thanks Will for your answer. Do you have a reference for determining the Galois representation from the Kodaira type for $p>5$?
May
8
asked Elliptic curves and supercuspidal representations of conductor $p^2$
Jan
27
awarded  Nice Question
Jan
10
awarded  Nice Answer
Dec
20
awarded  Nice Answer