8,013 reputation
11950
bio website perso.ens-lyon.fr/…
location Lyon
age 35
visits member for 4 years, 11 months
seen 9 hours ago

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...).


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
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revised calculate function from its divizor
Updated link