Peter Mueller
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Registered User
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I'm a professor of mathematics at the University of Würzburg (Germany). For further infos see my web page.
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Jun 12 |
awarded | ● Enlightened |
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Jun 12 |
accepted | A conjecture in Number Theory |
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May 17 |
comment |
Good effective versions of theorems of Artin and Brauer If nobody here has an idea or reference, you might ask Robert Boltje (boltje.math.ucsc.edu), he did some work on various aspects of Brauer's induction theorem. |
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May 15 |
accepted | A generalisation of the theorem of Maschke |
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May 14 |
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Simplifying an algebraic integer expression @Randall: Isn't your question essentially the same one as your question mathoverflow.net/questions/24513/… from 3 years ago? How are your numbers $pxy$ given, by minimal polynomials or complex floats up to some precision? |
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May 14 |
answered | A generalisation of the theorem of Maschke |
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Apr 26 |
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Rational functions with a common iterate @Anixx: Maybe because it is not clear at all what you are suggesting. (I didn't downvote though.) It seems to me that your approach more or less only works if you can compute a closed expression for the higher iterates - which is trivial in your examples - but impossible in general. |
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Apr 22 |
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A question from complex analysis @bo.gu: I do not understand your question. Are you asking how I did find the counter-examples, or do you want to know why these polynomials yield counter-examples? |
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Apr 20 |
accepted | A question from complex analysis |
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Apr 19 |
revised |
A question from complex analysis added 274 characters in body |
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Apr 19 |
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A question from complex analysis Sorry, I fixed the typo. |
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Apr 19 |
revised |
A question from complex analysis fixed typo |
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Apr 19 |
answered | A question from complex analysis |
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Apr 16 |
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Tame morphism from a curve to $\mathbb{P}^1$ @Will: $S^4$ is meant to be the symmetric group on $4$ letters? Anyway, in this characteristic $2$ context without Riemann's existence theorem, it isn't clear to me that this cover exists. I would be more convinced if one would write it down explicitly for an elliptic curve in Weierstrass form. |
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Apr 7 |
awarded | ● Enlightened |
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Apr 7 |
accepted | Inequality with Euler’s totient function |
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Apr 4 |
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Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal? @James D. Taylor: I changed my answer, so your comment probably does not apply anymore. |
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Apr 4 |
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Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal? Reformulated the answer, dropped the trivial part. |
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Apr 3 |
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Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal? How could it help here? The base fields are ^number fields^. Even over $p$-adic fields, the Krasner lemma only gives a sufficient, but not a necessary criterion for equality of fields. |
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Apr 3 |
revised |
Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal? Enhanced answer; added 4 characters in body |
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Apr 3 |
revised |
Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal? deleted 196 characters in body |
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Apr 3 |
answered | Is there a nice criterion for when the splitting fields of two irreducible polynomials are equal? |
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Apr 3 |
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Books on advanced galois theory Look at the list of books given in en.wikipedia.org/wiki/Inverse_Galois_theory In addition to that, also the book Field Arithmetic by Fried and Jarden contains quite a bit of (infinite) Galois theory. Furthermore, Algebraic Patching by Jarden is mostly about a relatively recent technique in Galois theory. |
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Apr 1 |
accepted | Simple field extension and rational points |
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Apr 1 |
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Simple field extension and rational points I extended the answer, hope it is clearer now. |
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Apr 1 |
revised |
Simple field extension and rational points Extended the argument in view of a comment. |
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Mar 31 |
revised |
Simple field extension and rational points improved proof, better readability |
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Mar 31 |
answered | Simple field extension and rational points |
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Mar 29 |
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irreducible polynomials with arithmetic progression coefficients @Aaron: Of course, there are many obvious examples like this: If $x-x_0$ is to be a factor of $f_{a,b}(x)=\sum_{k=0}^n(a+bk)x^k$, then there is a linear equation for $a,b$ from $f_{a,b}(x_0)=0$. |
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Mar 29 |
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irreducible polynomials with arithmetic progression coefficients @Greg: My comment does not contribute to the question at all. The question wants $a,b$ fixed and $n$ running, while my comment is about $n$ fixed and $a,b$ varying. |
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Mar 29 |
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irreducible polynomials with arithmetic progression coefficients @David: I think that Will fixes $n$. And then it is certainly a consequence of Hilbert's irreducibility theorem, since $\sum_{k=0}^n(a+bk)x^k$ is irreducible over $\mathbb Q(a,b)$, for variables $a,b$. |
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Mar 27 |
accepted | Fixed points of group action |
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Mar 27 |
awarded | ● Nice Answer |
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Mar 26 |
revised |
Fixed points of group action Adapted answer to the edit of the question; deleted 1 characters in body |
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Mar 26 |
answered | Fixed points of group action |
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Mar 18 |
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Principal maximal ideals in Z[x]/(F) $x^4-4x^2+9$ seems to be a promising candidate. |
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Mar 18 |
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Principal maximal ideals in Z[x]/(F) I think $F=x^4-10x^2+1$ doesn't work either, for $f=x+2$ is a divisor for $F$ mod $23$, but $23=(x^3 - 2x^2 - 6x + 12)f-F$. |
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Mar 18 |
accepted | Hurwitz’s construction of simple covers |
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Mar 18 |
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Principal maximal ideals in Z[x]/(F) Why the downvote - looks like an attractive question to me! (Now compensated by an upvote) |
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Mar 18 |
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Hurwitz’s construction of simple covers I don't mind getting a downvote - but still, a short explanation would be fine ... |
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Mar 18 |
answered | Hurwitz’s construction of simple covers |
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Mar 17 |
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All and the only algebraically closed fields s.t. any regular n-by-n matrix has a k-th root for every k I don't know a reference, but I'm pretty sure that it should be at many places. Maybe mostly only over the complex numbers, but that doesn't make a difference. All we need is that the binomial coefficients $\binom{1/k}{i}$ exist in the base field. |
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Mar 17 |
accepted | All and the only algebraically closed fields s.t. any regular n-by-n matrix has a k-th root for every k |
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Mar 17 |
answered | All and the only algebraically closed fields s.t. any regular n-by-n matrix has a k-th root for every k |
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Mar 16 |
revised |
Subgroups of the general linear groups added 332 characters in body |
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Mar 16 |
answered | Subgroups of the general linear groups |
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Mar 8 |
revised |
Bolza curve admits no anticonformal fixedpointfree involution added 43 characters in body |
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Mar 8 |
revised |
Bolza curve admits no anticonformal fixedpointfree involution added 1611 characters in body |
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Mar 7 |
answered | Bolza curve admits no anticonformal fixedpointfree involution |
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Mar 7 |
answered | From reducible polynomial to an irreducible one |
