Loïc Teyssier
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 1d reviewed Approve Hilbert's 17th Problem for smooth functions 2d reviewed Approve Need a help solving a rational integral 2d reviewed Approve Need a help solving a rational integral 2d comment Does the formal power series solution to $f(f(x))= \sin( x)$ converge? @WillJagy Yes, I know your answer (and am aware of work of Écalle), I think there is a little quiproquo here :) Originally Dmitrii posted this as an answer, where I originally commented (I didn't intend to comment in the main post). I just wanted to point out that I didn't see a clear way of making Dmitrii's argument to work, unlike Écalle's approach which is similar (using Abel's functional equation) but has been precisely developed in the Borel plane where the presence of singularities prevent the original series from converging. But I didn't want to repeat your answer, so didn't elaborate. 2d reviewed Approve Is the sum $\sum\limits_{j=0}^{k-1}(-1)^{j+1}(k-j)^{2k-2} \binom{2k+1}{j} \ge 0?$ Feb 10 comment Techniques to solve logarithmic functional equations Have you checked this question out, and other questions asked on this site about half-iterates? Feb 10 comment What area of maths have I reinvented? Arbitrary bijections don't respect the sum. A good starting friend here could be Riemann_series_theorem. Feb 10 reviewed Approve Uniform convergence of long geodesic to Liouville measure Feb 10 reviewed Approve Has anyone seen these binary trees (Catalan-type related to the Gegenbauer polynomials and Motzkin paths)? Feb 10 reviewed Approve Is there a proof that OEIS-A002387 is $[ e^{n-\gamma} ]$? Feb 10 reviewed Approve Consecutive numbers with mutually distinct exponents in their canonical prime factorization Feb 10 reviewed Approve Are all counterexamples of OEIS A226181 both Poulet numbers and Proth numbers? Feb 9 comment Understanding the steps taken in a calculation of the maximum profile likelihood of a simple ODE, given some data This is not the right site, as your question is not research level. Feb 9 comment How to find singularities from data and find monodromy group from singularities and differential system? A singularity is where the differential system has a pole or an indetermination / lack of regularity. Questions 3 you ask is highly non-trivial, even in the context of linear systems. Except in dimension $2$, I don't think one knows of an algorithm taking as input the equation and outputting the monodromy or differential Galois group. Question 4 is more tractable, there exist methods in differential algebra to find a polynomial differential equation satisfied by a given algebraic (or more elaborate) function. But I fear that you're taking the whole problem from a bad angle. Feb 7 comment Does the formal power series solution to $f(f(x))= \sin( x)$ converge? @DmitriiKouznetsov As far as I know an essential singularity is the centre of a small punctured disk on which a function is holomorphic. This does not seem to be the case (and the link you give does not claim such a thing). Yet your heuristic argument may not work since to get the $1/2$-iterate of $\sin$ you need to apply the inverse of the Abel function, which is multivalued, who knows how this result is going to give you a nice power series in integer powers of $z$,or any information on its convergence for that matter? Feb 6 comment A simple question about ordinary diffential equations of first order Your question is not silly, but it does not match the scope of this website. Try MathStackExchange where your question is likely to be better received. Feb 5 comment My question is about Constructions Please, don't answer questions like this one on this website. Feb 1 reviewed Approve Is hyperelliptic cryptography “practical”? Feb 1 reviewed Approve A categorical method to, say, determine the cardinality of a group Feb 1 comment pizza lemma (topology) Regarding the «cake lemma», I think it depends on the non-crossing permutation on 3 elements induced by the pairing between the 6 points of the boundary $A_0,\ldots,A_5$. Assume for instance that $A_j$ are ordered as successive points on the boundary, and that you connect $A_0, A_1$, then $A_2, A_3$ and finally $A_4, A_5$, I fail to see how you can send the arcs to three parallel lines.