born
Reputation
553
Next privilege 1,000 Rep.
Create new tags
 Mar 6 comment Can a vector component contain values that are not from the space's field? I assume that you mean the field of rational numbers $\mathbb Q$ - not any field - ecause you say that $\sqrt{2}$ is not an element of it? Mar 6 comment what is simplify, of $\sin^{-1}\tanh\theta=?$ I think, you missed an $=$-sign and something on the right hand side of the equation. Mar 1 comment Bounding the number of nonzero coefficients in a conic combination but how do you make sure that none of the coefficients of this linear combination is less than $0$? Feb 21 comment Serre's proof that zeta function is meromorphic I don't see how this implies $|\phi_n(s)|\leq\frac{|s|}{n^{x+1}}$ and what it has to do with the derivative. 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 $_{\mathbb{Q}}$"? 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 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