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location Harvard University, Cambridge, MA
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visits member for 2 years, 11 months
seen 13 hours ago

Héctor para los amigos (Pastén para los más amigos, Pasten para los extraños).


Aug
24
comment Philosophy behind Mochizuki's work on the ABC conjecture
Apparently, this answer written in September 2012 turned out to be not-so-unrelated to the question. See kurims.kyoto-u.ac.jp/~motizuki/…
Aug
17
comment For which rings $A$ is $A-\{0\}$ Diophantine over $A$?
Read the following paper by L. Moret-Bailly: Sur la définissabilité existentielle de la non-nullité dans les anneaux, Algebra and Number Theory. vol. 1, n° 3 (2007), 331-346.
Jul
29
awarded  Autobiographer
Jul
29
revised Genus of a plane curve of the form $\prod_{i=1}^n (a_iX+b_iY+Z) = Z^n$
edited body
Jul
29
answered Genus of a plane curve of the form $\prod_{i=1}^n (a_iX+b_iY+Z) = Z^n$
Jul
22
comment When is the image of an integral polynomial contained in the image of another?
I should mention that the idea in this argument is a particular case of the previously mentioned paper of Davenport-Lewis-Schinzel, where a more general result is proved using HIT.
Jul
21
comment When is the image of an integral polynomial contained in the image of another?
I think that using the suggested results will only lead to complicated issues of rationality and a lengthy case-by-case analysis on the pairs in the paper of Bilu and Tichy. See Theorem 1 in: H. Davenport, D. J. Lewis, A. Schinzel, Polynomials of certain special types. Acta Arith. 9 (1964), 107-116 for a result better suited for this problem.
Apr
20
awarded  Enthusiast
Apr
15
comment Generalization of proposition of Granville related to abc conjecture
What my comment hints is a way to prove the bound with $+1$ (using what one knows in the 1-variable case). You understood something different, but this misundertanding is actually interesting (unless I misunderstood my own comment).
Apr
13
comment Generalization of proposition of Granville related to abc conjecture
Except for the "+2" (which requires finer analysis on pencils in $\mathbb{P}^2$) a bound of this sort might be proved as follows: a general linear substitution $u=at+b$, $v=ct+d$ will preserve the degree of $r,s$, the coprimality of $r,s$, and cannot increase the degree of $rad(G(r,s))$.
Apr
4
answered Decidability of sum of powers exponential diophantine equation
Feb
7
comment Paths in $\mathrm{Spec} \, \mathbb{Z}$ and Kim's proof of Siegel's theorem for $\mathbb{P}^1 \setminus \{0,1,\infty\}$
As of today, I don't think that such a bound is known to follow from Kim's proof. Nevertheless, there is some work on computing the various objects involved in the proof, in order to get effective finiteness, see for instance 1209.0640v3
Feb
7
comment What is an étale theta function?
This question is an extremely valuable contribution, regardless of how well posed it is, or what is this web-site for. Regardless of the official policy, please just keep this question, thanks.
Feb
3
comment Paths in $\mathrm{Spec} \, \mathbb{Z}$ and Kim's proof of Siegel's theorem for $\mathbb{P}^1 \setminus \{0,1,\infty\}$
About clarifying the idea of paths: did you try reading this? people.maths.ox.ac.uk/kimm/papers/leeds.pdf
Nov
19
comment Is there a general connection between value distribution and zero distribution for functions representable by Dirichlet series?
Possibly unrelated comment: If instead of strips you use discs of increasing radii then the property that you want is false but it has a reasonable fix: add proximity functions and use the first main theorem of Nevanlinna theory. If you allow different (fixed, finitely many, at least 3) choices of z then you don't need proximity functions (second main theorem).
Nov
11
awarded  Nice Answer
Nov
10
answered Images of polynomials
Nov
10
comment Pairs of quadratic polynomials taking values pairs of consecutive squares
Interesting. Have you tried to do something? Do you have any guess?
Nov
6
answered Faltings height in short exact sequences
Nov
5
comment Is rigour just a ritual that most mathematicians wish to get rid of if they could?
Feel free to down-vote, but I could not resist: youtube.com/watch?v=aX6XMIldkRU