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visits | member for | 1 year, 10 months |
seen | 2 hours ago | |
stats | profile views | 7,893 |
Jun 2 |
answered | $L^1$ norm of exponential sum of $n^2 x$ |
Jun 2 |
reviewed | No Action Needed A riddle of marbles, buckets, and bottles |
May 31 |
reviewed | No Action Needed Rate of convergence of an algebraic irrational rotation |
May 30 |
reviewed | No Action Needed How to show whether a given knot and its mirror image are the same or not? |
May 28 |
comment |
The sum of squared logarithms conjecture
@JohannesHahn: I'm surprised by your comment. The question clearly states a conjecture and asks for a proof -- what's not on topic about this? And, anyone who doesn't want the gold can pass it on to me! |
May 27 |
reviewed | Leave Closed If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general? |
May 27 |
reviewed | Close What exactly is wrong with this statement (Lucas-Penrose fallacy)? |
May 26 |
comment |
Radial limit does not exist almost everywhere
@MattYoung: Slightly more general version -- lacunary Fourier series with coefficients whose $\ell^2$ norm is infinite. Is that what you looked at, or with coefficients being $1$? |
May 26 |
revised |
Radial limit does not exist almost everywhere
Added top level tag |
May 26 |
revised |
Radial limit does not exist almost everywhere
Corrected a small error |
May 26 |
comment |
Radial limit does not exist almost everywhere
@GHfromMO: Thanks for pointing that out -- I'll correct it. For the second part, my idea would be to compute moments on the circle with radius $r$. Since the powers of $2$ don't have too many linear relations, one would get an approximately (complex) Gaussian with variance tending to infinity (this is because of the assumption on coefficients). Then it follows that on each circle of radius sufficiently close to $1$, most points (measure close to $1$) will have a large value of the function. From that the result follows. |
May 26 |
comment |
On the number of consecutive divisors of an integer
@CaptainDarling: Note it's $\exp(-(\log z)^{2+o(1)})$, not like $\exp(-z^2/2)$ (Gaussian). I don't expect it to be anything nice. |
May 26 |
answered | Radial limit does not exist almost everywhere |
May 26 |
answered | On the number of consecutive divisors of an integer |
May 26 |
reviewed | Close If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general? |
May 26 |
comment |
Radial limit does not exist almost everywhere
Note that almost every real number $\theta$ will have the property that its binary expansion will have arbitrarily long strings of zeros. Now suppose $N$ is such that $\Vert 2^N \theta \Vert \le 2^{-h}$, and consider $f(e^{-1/2^N} e^{2\pi i\theta})$ and $f(e^{-1/2^{N+h}} e^{2\pi i \theta})$. They should differ by $\gg h$, showing that radial limits don't exist. |
May 25 |
reviewed | No Action Needed Is there any topological information encoded by the zero locus of a complex Hessian? |
May 25 |
reviewed | No Action Needed Meager subgroups of compact groups |
May 25 |
reviewed | Leave Open Numbers represented by inhomogeneous forms |
May 23 |
reviewed | Close $\mathcal S'(\mathbb R^d)$ is separable |