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visits | member for | 2 years |
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stats | profile views | 8,216 |
Apr
23 |
awarded | Enlightened |
Apr
23 |
awarded | Nice Answer |
Apr
23 |
reviewed | Close Quadratic - Ternary Forms |
Apr
22 |
comment |
About the convergence rate for an approximation to the heat kernel
As I pointed out in a comment below, this does follow from what I wrote. For $t/\epsilon >1$ use the earlier solution, which provides a stronger bound. For $t/\epsilon \le 1$, just use display (1) from my answer which then produces a bound of $e^{-t/\epsilon} + C (t/\epsilon) (1+|\log (t/\epsilon)|)$ which again is stronger than what you want. |
Apr
22 |
comment |
About the convergence rate for an approximation to the heat kernel
If you are interested in $t/\epsilon$ small, then just use (1) from above, and note that only the term $k=1$ there is important. This will give a bound of $O(1)$ in the range $t/\epsilon$ small, which again is better than what you want. |
Apr
22 |
comment |
About the convergence rate for an approximation to the heat kernel
But $1/2$ is better than $1/3$! You are assuming that $\epsilon/t$ is small, and so $(\epsilon/t)^{1/2} \le C (\epsilon/t)^{1/3}$ for some constant $C$. |
Apr
22 |
comment |
Prime races à la Mertens
See also mathoverflow.net/questions/150473/… |
Apr
22 |
answered | Examples of Maass forms with eigenvalue 1/4 |
Apr
22 |
reviewed | Reject nontrivial theorems with trivial proofs |
Apr
22 |
reviewed | Reject nontrivial theorems with trivial proofs |
Apr
22 |
reviewed | Reject nontrivial theorems with trivial proofs |
Apr
21 |
comment |
Is it meaningful to work on convergencies, integration, etc. on the Zariski topology?
Another one from MSE which seems (at least to me) to formulate the question more clearly: math.stackexchange.com/questions/53852/… |
Apr
21 |
reviewed | Approve What is the best lower bound for 3-sunflowers? |
Apr
20 |
reviewed | No Action Needed Concurrency related problems in $n$ independent, parallel $M/M/1$ queues |
Apr
20 |
revised |
Congruence for the number of points in the elliptic curve $y^2 = x^3+b \pmod{p}$
added 549 characters in body |
Apr
20 |
answered | Congruence for the number of points in the elliptic curve $y^2 = x^3+b \pmod{p}$ |
Apr
20 |
comment |
Congruence for the number of points in the elliptic curve $y^2 = x^3+b \pmod{p}$
The second result you mention goes back to Gauss, and is related to writing $p$ as a sum of two squares. Jacobi seems to have discussed identities related to the first congruence, which as Alison Miller notes above is related to $x^2+3y^2$. This paper by Hudson and Williams discusses these and other such congruences using Jacobi sums: ams.org/journals/tran/1984-281-02/S0002-9947-1984-0722761-X/… |
Apr
19 |
reviewed | Close Is it meaningful to work on convergencies, integration, etc. on the Zariski topology? |
Apr
19 |
answered | About the convergence rate for an approximation to the heat kernel |
Apr
18 |
reviewed | Approve What was the Question that led Euler to his Investigations on Polyhedra? |