# marlu

Cambridge, United Kingdom

Age: 22

I am a Part III student in Cambridge, focusing on Algebraic Number Theory.

 May 15 accepted Category of adjunctions inducing a particular monad May 15 asked Category of adjunctions inducing a particular monad May 6 awarded Caucus Apr 17 comment Alternating sum of multiple zetas equals always 1?The proof doesn't generalize to non-integer arguments since $z_m = x^{m-1}y$ only makes sense if $m$ is a natural number. But maybe the result for natural $m$ implies the result for non-integer $m$ by the identity theorem. If $m \mapsto 1-A_m$ is holomorphic on a connected open subset $D$ of the Riemann sphere containing $\mathbb N$ and the point at infinity, then since $\mathbb N$ has the point at infinity as limit point, the identity theorem forces $1-A_m$ to vanish on all of $D$. Apr 17 revised Alternating sum of multiple zetas equals always 1?fixed an error Apr 17 answered Alternating sum of multiple zetas equals always 1? Apr 16 answered field extension is Galois extension if and only if this extension are both normal extension and separable extension Apr 7 comment $f \in K[X]$ of degree $n$ with Galois group $S_n$, why are there no non-trivial intermediate fields of $K \subset K(a)$ with $a$ a root of $f$?You're right, that case needs to be taken care of separately. See the edit in my answer. Apr 7 revised $f \in K[X]$ of degree $n$ with Galois group $S_n$, why are there no non-trivial intermediate fields of $K \subset K(a)$ with $a$ a root of $f$?fixed the proof Apr 7 answered $f \in K[X]$ of degree $n$ with Galois group $S_n$, why are there no non-trivial intermediate fields of $K \subset K(a)$ with $a$ a root of $f$? Mar 28 revised Proof on p. $16 \;$ of Lang's Algebraic Number Theory\mathfrak B should be \mathfrak P Mar 28 answered Proof on p. $16 \;$ of Lang's Algebraic Number Theory Mar 19 comment Inverting formal power series wrt. compositionActually, I couldn't find a reference for that variant of Hensel's lemma. However, lemma 10.5 here (people.ds.cam.ac.uk/eb525/ec-notes.pdf) comes very close and I think the proof generalizes to the variant given above. Alternatively, look at lemma 11.6. This is exactly the statement you want to prove, and the proof actually goes along the lines of Hensel's lemma, by constructing successive approximations of the inverse power series. Integrality of $A$ is only needed for the uniqueness in Hensel's lemma, but since we didn't use that, it can probably be dropped. Mar 19 revised Inverting formal power series wrt. compositionfixed typo Mar 18 answered Inverting formal power series wrt. composition Mar 18 answered Holomorphic function $f$ such that $f'(z_0) \neq 0$ Mar 18 answered Kernel of $p$-adic logarithm. Mar 18 awarded abstract-algebra Mar 15 answered number of distinct prime Ideal of a ring Mar 11 comment Is all algebraic commutative operation always associative?See also here: math.stackexchange.com/questions/160945/…