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visits member for 2 years, 8 months
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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
Sep
5
awarded  Yearling
Jul
14
comment how to find cubic polynomial that an unknown subset of a set of integers satisfies
Is there a particular reason related to your application for suspecting that the coefficients are integers (rather than any integer-valued cubic, which can introduce some small denominators)? It would be interesting to know where does the problem come from (only if this is not top-secret information, of course).
Apr
28
comment How many solutions to $2^a + 3^b = 2^c + 3^d$?
Let me complement this answer, for the first step: to show that 2^a-2^c and 3^b-3^d are nearly "pure powers" you can use a lemma of Hensel (sometimes known as lifting the exponent lemma) instead of linear forms in log's. For instance, say that c<a, then c is the 2-adic valuation of (3^b - 3^d) and you can bound it with the lemma (linear forms in p-adic logarithms also work here).
Apr
28
comment Possible counterexample to a theorem assuming Lang's conjecture
At some point, I did check it (including Vojta's paper) and indeed, one just want evaluate the quadrics az^2+bz+c at 8 given points. In this paper, the 8 points are the squares of the alphas.
Apr
23
comment Units of $\mathbf Z[X,Y]/(P(X,Y))$
One can give an upper bound for the rank in terms of the places where poles are allowed (poles in the sense of valuations) by adapting the classical proof for rings of dimension 1. To deal with poles at geometric places, one can use as inspiration the analysis in J. Denef, The Diophantine problem for polynomial rings of positive characteristic. Logic Colloquium '78 (Mons, 1978), pp. 131–145
Apr
19
answered l-functions of calabi-yau varieties
Sep
18
comment Is the field of constructible numbers known to be decidable?
Write to Videla and ask him. He surely knows the state of the art and he will be happy to answer; he is a very nice person. As I understand, the problem is open and there is a group of people (including Videla) looking into it.