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bio website wallenborn.net
location Bonn, Germany
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visits member for 2 years, 9 months
seen Dec 1 at 17:20

Feb
21
accepted Set of locations where the Hilbert symbol is not equal to $1$
Feb
15
revised counterexample for: integral forms that are equivalent as rational forms are also equivalent as integral forms
added 10 characters in body
Feb
15
asked counterexample for: integral forms that are equivalent as rational forms are also equivalent as integral forms
Jan
7
comment Linear Algebra- independence and dependence
When you speak about a vetorspace you always have to say what your "base field" is. That is the set where the scalars come from. In high school we are normally used to the vectorspace $\mathbb{R}^n$ which we normally consider "over the field $\mathbb{R}$", but in general the base field can be everything (for example $\mathbb{F}_2$ or $\mathbb{Q}$) and $V$ does not need to be a power of the field $\mathbb{F}^n$.
Jan
7
comment Linear Algebra- independence and dependence
Is $V$ a vectorspace over some arbitrary field? Then you cannot divide by $2$ (or at least you have to handle this case separately).
Jan
6
comment Set of locations where the Hilbert symbol is not equal to $1$
Thank you for all your suggestions! I'll think about the name "set of ramified places". But since $p$-adic number theory is not my main focus, I don't know if this name is too fancy. @KCd and CamMcLeman: Am i getting it right that the Hilbert radical is the product of all the $v\in E_{a,b}$? May I furthermore ask if there is a common notation for the "Hilbert support of $<a,b>_{\mathbb{Q}}$"? Or is something like $E_{a,b}$ convenient?
Jan
6
comment Set of locations where the Hilbert symbol is not equal to $1$
@KCd: My question was not very precise, I wanted to ask if there is a common name and a common notation :-)
Jan
6
comment Set of locations where the Hilbert symbol is not equal to $1$
@CamMcLeman thanks for editing!
Jan
6
comment Set of locations where the Hilbert symbol is not equal to $1$
@Michalis: yes, you are totally right
Jan
5
asked Set of locations where the Hilbert symbol is not equal to $1$
Jan
5
answered Definite integral involving $\sqrt{\log}$
Dec
31
asked Hilbert symbol over a ring
Dec
4
accepted $p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.
Dec
3
comment $p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.
ah, now everything is clear \o/ thank you very much!
Dec
3
comment $p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.
maybe I'm wrong but $(u-x_0^2)/p=x_1^2p+2x_1x_0$ (so the $x_1$ has a square) and therefore it is not a linear equation and does not need to have a solution. And i still don't see that all this has to do with $u$ being a unit or not :-/
Dec
3
comment $p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.
why exactly is $x_1$ determined uniquely by $(x_1p+x_0)^2\equiv u \pmod{p^2}$? I see, that $p, x_0$ and $u$ are given but I don't see why such an $x_1$ must exist.
Dec
3
comment $p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.
I hoped, that I could avoid this sort of inductive argumentation. I'll lock over it and accept your answer. Thanks a lot!
Dec
3
comment $p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.
where do I use that $u$ is a unit, when $0<y$? For this direction, we may assume that $u_0$ is a quadratic residue modulo $p$ which by definition means that there is an element $y$ not zero less then $p$ such that $y^2=u_0$. It's a statement for rational integers and I don't see why it is important that $u$ is a unit in the $p$-adic integers.
Dec
3
asked $p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.
Nov
5
answered Is there a special name for the operands of a multiplication?