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Newest
 Yearling
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Jun
30
asked Is the structure constant additive on connected components?
Jun
16
comment What is the order of a cusp form at a cusp?
Thanks! I've been a bit confused by the general sloppiness that seems to permeate this issue...
Jun
16
asked What is the order of a cusp form at a cusp?
Apr
27
comment When are heat kernels only dependent on the distance?
Thanks for your answer! You address a point I'm eager to explore, but unfortunately I do not fully understand your answer. Specifically, I do not see the statement "for a same amount of time, at least for small times, the heat from q2 in the flat part of M will be more spread out than the heat from q1 in the thin part". This seems to be in contradiction with Varadhan's large deviation formula (on a complete manifold): $$\lim_{t \rightarrow 0} -4t \log(K(t;x,y)) = d(x,y)^2.$$ In order to mark your answer as accepted, could I ask you to elaborate a but more please? Thanks again and +1!
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?