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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 not-so-weak Goldbach's conjecture
May
23
reviewed Close Are there “adelic” L-functions?