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Sep
3
comment 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
comment 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
comment 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
comment 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
comment 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 $b<a<8b$.