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2d
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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Nov
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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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Nov
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asked “simulteneous eigenvectors” under the full set of weighted Laplacians on a $g$-fold product of the Poincare half plane
Nov
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awarded  Revival
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revised Characterizing the real analytic Eisenstein series
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Nov
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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
Nov
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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
Nov
16
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.
Nov
16
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 Stefan for the example. Now I can see why I could not prove it. So what kind of lower bound can you get as a function of $n$. Is $\sqrt{n}$ good enough?
Nov
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revised 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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Nov
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asked bounding from below the cardinality of a set of generators of the $n$-fold cartesian product group of a finite group
Nov
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comment closed integral formula for a non-zero solution of a homogeneous linear ODE of order 2
Dear Robert, I just had a look at Kuga's book. Basically, the answer to my question is positive if and only if the monodromy representation is triangulizable. Unfortunately, the book only proves the if direction (which is quite easy) and says that the only if direction is beyond the scope of the book. Do you know a reference off-hand where I could find a proof for the only if direction?