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bio website mat.ulaval.ca/hchapdelaine/…
location Quebec city
age 36
visits member for 4 years
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1d
comment Solving z^n=a+ib using only radicals of positive real numbers
Dear Alexander, I think that what was on my mind when I wrote this post was given $n\in\mathbf{Z}_{\geq 3}$ and $a,b$ algebraic real numbers, can you give a criterion which says when is $z^{n}-(a+bi)$ positive solvable.
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awarded  Self-Learner
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revised Solving z^n=a+ib using only radicals of positive real numbers
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comment Solving z^n=a+ib using only radicals of positive real numbers
Dear Alexander, already in the answer that I had posted on Sep 21, 2012, I was quoting Brian Conrad's note: "radical tower and roots of unity"
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revised “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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comment “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
So I understood well what is going on. The sketch of the proof in (b) is valid. In fact, the result is completely general. If one deals with a linear system of homogeneous ODE's in $g$ variables of order $n_1,n_2,\ldots,n_g$ (where ONLY ONE variable appears in each equation) then the solution space will be a vector space of dimension $n_1n_2\ldots n_g$ over the field of meromorphic functions in one variable. Of course this a very special kind of PDEs system.
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revised “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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revised “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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revised “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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revised “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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revised “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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revised “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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asked “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
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awarded  Revival
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revised Characterizing the real analytic Eisenstein series
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comment bounding from below the cardinality of a set of generators of the $n$-fold cartesian product group of a finite group
Thanks a lot @Derek for your argument which provides a logarithmic lower bound. I find it amazing that the order of magnitude of this (a priori) crude lower bound is the right one
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accepted bounding from below the cardinality of a set of generators of the $n$-fold cartesian product group of a finite group
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comment bounding from below the cardinality of a set of generators of the $n$-fold cartesian product group of a finite group
Hmm, I did not think much about it, but I find it counter-intuitive for the least.