Alexandre Eremenko
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 1d comment Algebraic invariants of linear ODE's with constant coefficients Can you be more specific: what do you exactly mean by "equivalence point transformations"? 2d comment Are there entire functions that are unexpectedly periodic? A special case of the theorem of Abel that I stated is that the inverse function to $\int dx/\sqrt{P(x)}$ is periodic, where $P$ is a polynomial of degree $3$ or $4$. Also, not many mathematicians before Abel could see this. 2d comment Are there entire functions that are unexpectedly periodic? Not all mathematicians before Euler were kids. 2d comment Are there entire functions that are unexpectedly periodic? Further generalizations of this fact are due to Weierstrass, Phragmen, Painleve and Myrberg. 2d comment Are there entire functions that are unexpectedly periodic? If you define $e^x$ as $\sum x^n/n!$ it is somewhat unexpected that it is periodic. As a generalization, every meromorphic solution of a differential equation $F(y',y)=0$ where $F$ is a polynomial, is either rational or periodic. This is due to Abel. Nov 20 comment When is an erratum necessary? If the mistake is serious you publish a correction, if it is not, you don't. You wrote this yourself. What other answer you are trying to obtain? How to decide what is serious and what is not? Who can decide this except yourself? Nov 19 comment Center of mass from the abstract point of view, or could the ancient Greeks invent modern analysis? Center of mass is not really a characteristic of a set, it is a characteristic of a measure. (This is implicitly contained in the answer of Deane Yang). Nov 19 comment Explicit analytic function with modulus asymptotic to $\Re z+\Im z$ @Iosif Pinelis: it is easier to prove than to find a reference:-) But look, for example to Valiron, Fonctions Analytiques Ch III, Sect 24 for an idea of a proof. Probably Hayman-Kennedy, Subharmonic functions is also OK. Both are available in Russian as well. Nov 19 comment Heat equation - regularity of solutions Yes. Just differentiate the heat kernel $\alpha$ times, and you can have it with $\alpha=0$. Nov 19 revised Explicit analytic function with modulus asymptotic to $\Re z+\Im z$ added explanation Nov 18 answered Explicit analytic function with modulus asymptotic to $\Re z+\Im z$ Nov 17 awarded Guru Nov 16 awarded Enlightened Nov 16 awarded Nice Answer Nov 14 comment Isometry group of a compact hyperbolic surface Also see the Wikipedia article "Hurwitz's automorphisms theorem". It has a nice discussion of the subject. Nov 14 comment Isometry group of a compact hyperbolic surface The bounds are attained (see the references that I included). I believe that the second question is addressed in the second reference (S. Levy). Nov 13 comment Filled level sets of harmonic funtions The complement of the filled level set of an entire function $\{ z:|f(z)|>M\}$ is not necessarily connected, example $f(z)=\cos z$, $M=2$. So what are you really asking? Nov 12 comment Does Gaussian Quadrature actually refer to Gauss-Legendre Quadrature？ When they say Gauss hey usually mean Gauss-Legendre (by default). Legendre was very unhappy because of this, and many other similar cases when his name is omitted btw. Nov 11 comment Is there a proof of the uniformization theorem using circle packing? One problem is this: what is a "circle" on an arbitrary Riemann surface? Nov 9 comment Is it possible to pursue a career in mathematics only working within a small subset of the subject? The short answer is "yes". One can make a career in mathematics by pursuing just one narrow area. Examples are abundant.