Shubhodip Mondal
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 Dec21 awarded Constituent Dec12 comment Product of sums equal to sum of products ${}{}{}{}{}{}{}{}$ Dec12 comment Product of sums equal to sum of products Yes.(I had 10 more to go.) Dec11 comment Ex. 1.3.10 in Tao's Additive Combinatorics Well yeah.But I you should check if image of 1/1-z is (contained in) a simply connected space not containing zero as f^k = exp k log f Dec10 comment If $f(z)$ is a polynomial function of degree $n \ge 2$, prove that the sum of the residues of $\frac{1}{f(z)}$ is zero Haha, or in order to do it directly, use Lagrange's Interpolation. Dec10 comment Ex. 1.3.10 in Tao's Additive Combinatorics added an answer. do you have any comments? Dec9 answered Ex. 1.3.10 in Tao's Additive Combinatorics Dec9 awarded Caucus Dec5 revised Investigate whether there exists a function $f : [a,b]\rightarrow R$ that is continuous and that takes exactly twice each of its values. edited body Dec5 answered Investigate whether there exists a function $f : [a,b]\rightarrow R$ that is continuous and that takes exactly twice each of its values. Dec5 comment Investigate whether there exists a function $f : [a,b]\rightarrow R$ that is continuous and that takes exactly twice each of its values. The accepted solution is not helpful Dec5 answered one-to-one holomorphic map of $\mathbb{C}$ onto itself must be of the form $az+b$? Nov30 revised If $f$ is ananlytic in $D_r(z_0)$\ {$z_0$} and $Ref(z)>0$ for all $z\in D_r(z_0)$\ {$z_0$} then $z_0$ is a removable singularity deleted 2 characters in body Nov30 answered If $f$ is ananlytic in $D_r(z_0)$\ {$z_0$} and $Ref(z)>0$ for all $z\in D_r(z_0)$\ {$z_0$} then $z_0$ is a removable singularity Nov27 revised $f$ is either univalent or constant added 62 characters in body Nov27 comment $f$ is either univalent or constant Rouche's theorem. Nov27 answered $f$ is either univalent or constant Nov24 answered Geometrical Interpretation of Cauchy Riemann equations? Nov24 revised fixed point for analytic function in a connect set eddited the problem to make w a domain Nov24 comment fixed point for analytic function in a connect set Why is this problem On hold? I can completely answer it when $\omega$ is simply-connected. If $\omega = \mathbb{C}$, the condition is not met. So, we can assume $\omega \ne \mathbb{C}$, and then the Riemann Open mapping theorem helps you to reduce the problem to a disk.. and then one can use Rouche's theorem to show that there is a unique fixed point.