Reputation
11,288
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
2 12 38
Impact
~139k people reached

5h
comment Show $ \int_0^\infty \frac{\sin ax \sin bx}{x^2} \, dx = \frac{\pi a}{2} $ if $ a < b$
my question is a duplicate: math.stackexchange.com/questions/441106/…
Apr
16
comment Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p) $
this did not depend on $p = 4k\pm 1$ ?
Apr
8
comment show that $\sum P(x,y) e^{x^2 + y^2}$ is a modular form over $\Gamma_0(4)$ where $P(x,y) = x^4 - 6 x^2 y^2 + y^4$
My best guess this comes from $f(x,y) = P(x,y) e^{-(x^2+y^2)}$ and saying $$ \sum_{(x,y) \in \mathbb{Z}^2} f(x,y) = \sum_{(x,y) \in \mathbb{Z}^2} \hat{f}(x,y)$$ which is Poisson summation in two variables and $\mathbb{Z}^2$ is a lattice dual to itself.
Apr
8
comment Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p) $
@anomaly covering map is fine. I reasoned for example that $\mathrm{Spin}(2) \to \mathrm{SO}_3$ is a 2-1 covering map for $\mathbb{R}$. And we have $\mathrm{Spin}_2 \simeq \mathrm{SU}_2$.
Apr
6
comment Show the Dedekind $\eta(\tau)$ function is a modular form of weight $\frac{1}{2}$ for $\Gamma_0(6)$
I have read that $\eta(\tau)^24$ is a modular form of weight 12 over $\mathrm{SL}_2(\mathbb{Z})$, so maybe $\eta$ is modular of weight $\frac{1}{2}$ ?
Apr
4
comment A set such that $A$, $A+A$ have density zero but $A+A+A$ has positive density.
Is that called log density? Not even. Like $\sqrt{\log}$ density.
Apr
4
comment A set such that $A$, $A+A$ have density zero but $A+A+A$ has positive density.
Finally $d(\square + \square + \square + \square) = 1$ as all positive integers can be expressed as the sum of 4 squares. So what is happening here?
Mar
24
comment $S=\frac{-d^2}{dx^2}$ self-adjoint operator or not?
I am a little bit confused by symmetric but not self-adjoint as this could never happen in finite dimensional space
Mar
22
comment equivalent to $A \to (C \leftrightarrow D)$
If $A$ is not true, then maybe $C$ and $D$ are not equivalent. In number theory, there are rings where "prime" and "irreducible" are not equivalent.
Mar
21
comment Ruler and compass question
how is this Galois theory?
Mar
20
comment sum of divisors function $\sum \tau(n) = \frac{1}{4}$
@Gerben Divergent series get hated on in math courses but I trudge on since I see them so often in physics courses.
Mar
18
comment How to visualize the region $\mathbb{H}/\Gamma_0(4)$ and its cusps?
math.stackexchange.com/questions/1288478/…
Mar
4
comment Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?
Notice that $n \geq 2$. In this guy's example $n \equiv 1$.
Feb
7
comment Show that $J_n(x)$ satisfies Bessel equation $ x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - n^2)y = 0 $
also math.stackexchange.com/questions/359107/…
Jan
29
comment Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \ $?
The paper that I am reading is unusual as they are cutting along $\mathbb{R}^+$ instead of $\mathbb{R}^-$ I should have mentioned that thanks.
Jan
29
comment Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \ $?
what if you cut at positive reals?
Jan
26
comment express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
Yeah this could be the one
Jan
25
comment express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
@tired yes. the $e^{\frac{1}{2g}}$ is an instanton correction
Jan
25
comment express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
@tired you get the error function if you don't add any correcting terms wolframalpha.com/input/… that's why I started making stuff up. it comes from a physics paper
Jan
24
comment How to prove that $f$ is integrable if $\forall \epsilon, \ \exists$ partition $M\in [a,b]$ such that $U_f(M) - L_f(M)\lt\epsilon$?
In practice these partitions might get pretty exotic. What partition makes the upper and lower Riemann sums close when $f(x)=\sum_{n=0}^{100}\frac{1}{n}\sin nx$ ? This converges to a sawtooth wave