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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