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Sep 3 |
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A conjecture about the measure estimates of a trigonometric polynomial
Wouldn't $(\sin x)(\sin 2t) - (\sin 2x) (\sin t)$ give a counter example? (Normalize this suitably to get $L^2$ norm $1$. The point is that if $x$ and $y$ are less than $\epsilon^{1/4}$ each, then the answer is still $\ll \epsilon$, so that the set of small values has measure about $\epsilon^{1/2}$ (and not $\epsilon^{\alpha}$ for any $\alpha<1$). |
Sep 3 |
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A conjecture about the measure estimates of a trigonometric polynomial
So why not edit to make the question clear. Having many unnecessary variables can be distracting. |
Sep 3 |
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A conjecture about the measure estimates of a trigonometric polynomial
Can't you simply take $\beta=1$ and then assert that the measure is bounded by $M\epsilon^{\alpha}$ for $\alpha <1$ and $\epsilon$ small enough? (All I've done is call $\epsilon^{\beta}$ as $\epsilon$.) This might be a little bit clearer. In any case, the question does seem reasonable to me, and I'll add my vote to reopen. |
Sep 2 |
revised |
$L^2$ discrepancy bound for sequences in $[0,1)$
edited tags |
Sep 2 |
answered | $L^2$ discrepancy bound for sequences in $[0,1)$ |
Sep 1 |
reviewed | Close Use a graphic tablet to write in Latex or MathML |
Sep 1 |
comment |
Uniformly permutation and the length of a size biased cycle
It seems to me that there are $n!$ variables -- the probabilities for each permutation -- but only $n^2+1$ equations. So for large $n$, surely this is false? (Of course the probabilities have to be non-negative ...) |
Aug 30 |
comment |
Asymptotic formula for the number of ways to write a number as the sum of $k$ triangular numbers
Multiply $n$ by $8$ and add $k$. Thus the problem is equivalent to representing $8n+k$ as a sum of odd squares, and all that you want to know has been worked out. For $k\ge 5$ there is no problem with using the circle method (or modular forms) -- the asymptotic is about $C(n) n^{k/2-1}$, where $C(n)$ is bounded above and below. For $k=4$, use Jacobi's work on sums of four squares. For $k=3$, Gauss related sums of three squares with class numbers. |
Aug 30 |
reviewed | Reopen How to find generators to Mordell weil groups of elliptic curves? |
Aug 30 |
reviewed | Close reference on aperiodicity and cluster |
Aug 29 |
reviewed | No Action Needed Proof of the Dunford-Pettis theorem |
Aug 29 |
reviewed | Reviewed How to find generators to Mordell weil groups of elliptic curves? |
Aug 28 |
reviewed | Leave Open Elliptic curves with trace of Frobenius values always congruent to 0 modulo 2 |
Aug 28 |
reviewed | Looks OK Game on the tree |
Aug 28 |
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Exponential Sum Bound
Dougal's link is valuable of course, but it's amazing to me that a reference to the paper gets more upvotes here than a response by the author himself. |
Aug 27 |
reviewed | Leave Open Prime order elements in $GL(n,\mathbb{Z})$ |
Aug 27 |
reviewed | Leave Open An angle-doubling trick of Kirillov and Berenstein |
Aug 27 |
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Dynamics in the integers - Floor function
For the second part use Weyl's equidistribution theorem which shows that the limit is $1-\alpha N$. |
Aug 26 |
reviewed | Leave Closed Proof without words for surface area of a sphere |
Aug 26 |
comment |
Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
I think $k$ is a about size $b$, which is roughly $\ell-m$. Knowing that this is at least $5$ doesn't help, or hurt, the computations of GH from MO. In the notation of the original question, GH from MO's computations have disproved the conjecture if the condition had been $b<a<8b$. |