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41m

reviewed  Leave Closed How to prove that $h^*(A)$ exists and $h^*(A)=\{x\in ON : x \leq^* A\}$? 
4h

reviewed  Close For which $x$ the inequality $ax+be^{x/2}>c$, where $a,b,c,x>0$ and $c>2b$ holds 
5h

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 $1$? 
5h

revised 
Radial limit does not exist almost everywhere
Added top level tag 
5h

revised 
Radial limit does not exist almost everywhere
Corrected a small error 
7h

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. 
9h

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. 
10h

reviewed  Close How to find the matrix of adjoint transformation R* according to the usual scalar product 
21h

answered  Radial limit does not exist almost everywhere 
21h

answered  On the number of consecutive divisors of an integer 
22h

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? 
1d

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. 
1d

reviewed  No Action Needed Is there any topological information encoded by the zero locus of a complex Hessian? 
1d

reviewed  No Action Needed Meager subgroups of compact groups 
1d

reviewed  Leave Open Numbers represented by inhomogeneous forms 
May 23 
reviewed  Close Matrix decomposition ( Kronecker product decomposition) 
May 23 
reviewed  Close $\mathcal S'(\mathbb R^d)$ is separable 
May 23 
reviewed  Close Implementation of almost integer to cryptography 
May 23 
reviewed  Leave Open A notsoweak Goldbach's conjecture 
May 23 
reviewed  Close Are there “adelic” Lfunctions? 