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English is not my native tongue. German is not my native tongue. French is not my native tongue.


19h
comment Counting number of points in a lattice with bounded sup norm
@SJY: I am glad I could help. If you find any of my posts useful, please drop me a point for it. Thanks!
1d
comment Counting number of points in a lattice with bounded sup norm
@SJY: The volume of $B$ is $\prod_{l=1}^j(t_l-r_l)$ times $Vol_j(B')$, where $B'=[0,1]v_1+\dots+[0,1]v_j$ is the parallelepiped spanned by the vectors $v_1,\dots,v_j$. In order to find $Vol_j(B')$, follow my comment of Apr 5 at 3:42. At any rate, you can read about the Lebesgue measure in many textbooks, e.g. in Rudin: Real and complex analysis.
1d
comment Counting number of points in a lattice with bounded sup norm
@SJY: The $j$-volume is the Lebesgue measure on the underlying $j$-dimensional subspace. I called it $j$-volume to distinguish it from the Lebesgue measure on the full space.
1d
comment Integer solution to the equation
I answered the problem in the negative. See below.
2d
comment Primes as uncorrelated random variables
The Wikipedia article does not use the word "proof" in that context. So the quotation mark is misleading here. Without the quotation mark, it would be equally misleading, so I suggest you change the first sentence. A more serious problem with your post is that it does not contain a well-formulated mathematical question. To clarify: no proof of Goldbach's conjecture would consider the primes random variables, because they are not random variables.
2d
comment An upper bound for the length of the continued fraction expansion of $\sqrt d$
@GeraldEdgar: In analytic number theory, $f(x)=\Omega(g(x))$ means that $f(x)=o(g(x))$ is false, and I followed that convention. See en.wikipedia.org/wiki/…
2d
revised An upper bound for the length of the continued fraction expansion of $\sqrt d$
added 134 characters in body
2d
answered An upper bound for the length of the continued fraction expansion of $\sqrt d$
Apr
16
awarded  Nice Answer
Apr
15
answered A variant of Goldbach Conjecture
Apr
15
comment What math do I need to know in order to understand basic trigonometry?
This site is for research level questions. For general questions in mathematics see math.stackexchange.com
Apr
14
revised Is every positive integer a sum of at most 4 distinct quarter-squares?
deleted 5 characters in body
Apr
14
revised Is every positive integer a sum of at most 4 distinct quarter-squares?
improved the presentation
Apr
13
comment Equivalence of Polignac to finite Goldbach?
@GerryMyerson: I think I got confused by history a bit. At any rate, Hardy and Littlewood did conjecture an asymptotic formula for Goldbach's conjecture, and they gave a heuristic for it in their paper "Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes". In the same paper, they also gave an asymptotic formula for Polignac's conjecture, with a similar heuristic and a similar shape. See Conjecture A (on page 32) and Conjecture B (on page 42) in the paper (available online as fuchs-braun.com/media/8cdd73c813c342f8ffff80d1fffffff0.pdf).
Apr
12
answered Equivalence of Polignac to finite Goldbach?
Apr
11
comment Has this strong number theoretic conjecture of Euler been proved, and where could I find such a proof?
Nice find indeed. A similar treatment can be found in euler.genepeer.com/eulers-pentagonal-number-theorem
Apr
11
revised Has this strong number theoretic conjecture of Euler been proved, and where could I find such a proof?
Fixed spelling.
Apr
10
comment On successive minima and basis of a lattice
@SJY: I don't know such an example.
Apr
9
revised Is $1/\max(i,j)$ a bounded matrix on Hilbert spaces?
fixed spelling
Apr
9
comment Is $1/\max(i,j)$ a bounded matrix on Hilbert spaces?
This is very nice!