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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?