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bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 2 months
seen 2 hours ago

Aged mathematician


Jun
27
comment Cassel's book on Elliptic Curves
I understand your position. Couldn’t you just prove it for two special cases: when $s$ is prime to $p$, so that the abs. val. in question is unchanged, and when $s=p$?
Jun
26
comment Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
Right, @HaraldHanche-Olsen, I guess the two are as alike as peas in a pod. Only thing is, that I had in mind a different enumeration of $\mathbb N\times\mathbb N$.
Jun
26
comment Cassel's book on Elliptic Curves
I don’t own Cassels’s book, and am not in a position to find one in a library. Would you accept an argument (undoubtedly different from Cassels’s) based on the formal group of the elliptic curve in question?
Jun
25
comment A group which multiplies input by 2
Like all of us when we’re just learning something or when we’ve been away from it for a long time, your ideas are confused and difficult to penetrate. Generally speaking, a group doesn’t do anything, it just sits there lookin’ pretty. So your wording “a group … which multiplies” throws most of us off very seriously. I guess you might spend some time thinking things through more clearly, and maybe rewrite your question.
Jun
25
answered How is $\mathbb{F}_4$ generated?
Jun
25
answered Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
Jun
25
comment The image of a conic section under the $z^2$ map
Indeed. You might consider editing your question to make it clearer just what you were asking.
Jun
25
comment If $f$ is continuous, so is $g=|f|$
Showing that the absolute-value map is continuous is easy enough: taking delta equal to epsilon will always work.
Jun
25
comment The image of a conic section under the $z^2$ map
Take a circle tangent at the origin to the $y$-axis. Isn’t the image of that something like a cardioid? It certainly has a cusp at the origin.
Jun
25
answered If $f$ is continuous, so is $g=|f|$
Jun
20
answered $f(x)=\log x\Leftrightarrow f^{-1}(x)=e^x$. Why $e=2.73\cdots$?
Jun
20
comment Why exponential function on p-adic numbers is meaningless?
Whoops, I should have also said that there is no pi in the $p$-adic world. How would you have defined it? It’s a real number, after all, and whatever definition you might take for the real number $\pi$ will be expected to make no sense in the $p$-adic world. For instance, though you can always take an (at most quadratic) extension of $\mathbb Q_p$ to have an $i$ in it, since the $p$-adic exponential function is never $1$ on its domain of definition (except at $z=0$), there will be no possibility for a nontrivial $z$ with $\exp(z)=1$, from which you’d have hoped to extract $\pi$.
Jun
20
answered Why exponential function on p-adic numbers is meaningless?
Jun
20
comment Can one check by hand whether the Tate module of an elliptic curve is semi-simple
And for the specific case of $y^2=x^3+1$, the imaginary field in question is $\mathbb Q(\omega)$, where $\omega^2+\omega+1=0$.
Jun
19
comment Questions about p-adic expressions.
Right here in the real numbers with decimal expansion, $1/11=.090909\dots$, the two sides don’t look similar, do they?
Jun
18
comment how to see the logarithm as the inverse function of the exponential?
Back in an earlier geological era, when I was teaching Calculus at Brown, a number of standard texts made the logarithm primitive, the exponential secondary. It’s perfectly easy to prove the log’s basic properties from the integral definition, then invert it and get the exponential and show its properties. I’ve forgotten whether we ever showed that the limit of $(1+x/n)^n$ is $\exp(x)$, though.
Jun
17
comment how to see the logarithm as the inverse function of the exponential?
The other common way is to introduce log as the integral of $1/x$, and define the exponential function as the inverse of that. I’m not aware of any presentation that introduces the functions separately and then shows that there is a relationship between them.
Jun
17
comment Why is the multiplicative group of a finite field cyclic?
In most cases, if you’re asking the question of why something is true, well, that’s the whole point of mathematics, and you should try to find a proof. If you can’t understand the proof (happens to all of us!), then you might ask here for help with understanding.
Jun
16
comment Can someone explain this exponent simplication ? $a^4 \equiv a^{2014} \pmod{31}$
Sure, $31$ is prime, and for every nonzero residue $\alpha$, you get $\alpha^{30}=1$. Result follows.
Jun
16
comment Question on Infinite Abelian Group
So what is your question?