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 Yearling
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Apr
24
revised When are heat kernels only dependent on the distance?
edited title
Apr
23
revised When are heat kernels only dependent on the distance?
added 1 character in body
Apr
23
asked When are heat kernels only dependent on the distance?
Apr
20
awarded  Yearling
Apr
2
answered If $a,b,c$ are integers such that $4a^3+2b^3+c^3=6abc$, is $a=b=c=0$?
Apr
2
awarded  Popular Question
Mar
27
comment Closed form for $\sum_{k=1}^\infty \frac{k+1}{q^{k(k+n)}}$
@nayrb Thanks, actually I tried to complete the squares, isolating then the $k^2$-factor, but the question I linked doesn't seem to provide any closed form for the series I'm interested into. Or am I missing something?
Mar
27
revised Closed form for $\sum_{k=1}^\infty \frac{k+1}{q^{k(k+n)}}$
deleted 6 characters in body
Mar
27
comment Closed form for $\sum_{k=1}^\infty \frac{k+1}{q^{k(k+n)}}$
Sorry, my fault, $q>1$!! I edit the question!
Mar
27
asked Closed form for $\sum_{k=1}^\infty \frac{k+1}{q^{k(k+n)}}$
Mar
25
asked Explicit value of $\overline{\mathcal{O}}_{\mathbb{P}^1(\mathbb{Z})}(1).\overline{\mathcal{O}}_{\mathbb{P}^1(\mathbb{Z})}(1) $
Mar
23
comment Fubini-Study norm of homogeneus polynomials
@TedShifrin Thanks! Evaluating $\int_{\mathbb{P^1}} \omega_{FS}$ is exactly what made me suspicious in the first place. By breaking the integral in the two domains $\{|\zeta_0|<1\}$ and $\{|\zeta_1|<1\}$ and switching to polar coordinates I reduce it to $2\cdot \int_0^{2\pi} \int_0^1 \frac{r}{(1+r^2)^2} dr \wedge d\theta$, which integrates to $2\pi \left[ \frac{r}{1+r^2} +\arctan(r)\right]_0^1 = \pi + \pi^2/4$. But this is not what I expected! On one hand I could ask you to check my computation, but on the other one it would be easier just to get a reference to somewehere where it's done!
Mar
23
asked Fubini-Study norm of homogeneus polynomials
Mar
1
comment Smoothly Equivalent Curves
I don't know what kind of regularity do you assume for curves; but if one of the two is only continuous and the other one is $\mathcal{C}^1$ they cannot be smoothly equivalent, otherwise the former would be $\mathcal{C}^1$ as well.
Feb
20
comment If $\{f_1,…,f_n\}$ generate $R$ then does $\{f_1^N,…,f_n^N\}$
@user26857 Thanks! I'm sorry for the sloppiness in the example, I just tried to rapidly concretize a stomach feeling...
Feb
19
comment If $\{f_1,…,f_n\}$ generate $R$ then does $\{f_1^N,…,f_n^N\}$
But if the ring does not have a unity I think the statement is false. Indeed one can consider the ring of even integers, which is generated by $2$ but not by $4$. Right?
Feb
15
comment Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
@Mary Star I edited the answer to extend the hint.
Feb
15
revised Lebesgue-Integrability of $x \mapsto \frac{\sin x}{x}$
I extended the hint, as requested by the OP.
Feb
14
comment Show that the space $C^{0, \gamma}(U)$ is complete
All your last 10 questions (not to go too far in the past) received an upvoted answer, none of them got accepted. Would you mind either accepting them or let the answerers know how they can improve on their work? Thanks for your cooperation.
Feb
11
comment Function for encryption/decryption - What is $n \phi(n)$?
All your last 10 questions (not to go too far in the past) received an upvoted answer, none of them got accepted. Would you mind either accepting them or let the answerers know how they can improve on their work? Thanks for your cooperation.