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visits | member for | 1 year, 10 months |
seen | 3 hours ago | |
stats | profile views | 7,894 |
Mar 23 |
reviewed | Close Intuition about poisson summation formula? |
Mar 22 |
reviewed | Leave Open Does anyone recognize this generating function |
Mar 20 |
comment |
Asymptotics of special square-free numbers
See Exercise 4 of Section 7.4 of Montgomery and Vaughan's book on Multiplicative number theory. If $k$ is fixed, then the asymptotics are essentially the same as that of just numbers with $k$-prime factors (forgetting squarefree). |
Mar 20 |
reviewed | Leave Open Discriminant of a compositum of number fields, a bound? |
Mar 19 |
answered | Angular equidistribution of lattice points on circles |
Mar 18 |
answered | Number of representations of an integer as an (arbitrary) sum of products |
Mar 18 |
reviewed | Close derivatives of composite function |
Mar 18 |
reviewed | Close Need help publishing a mathematical proof? |
Mar 17 |
comment |
When does Merten's product theorem accurately estimate the number of coprimes in an interval?
Great; glad you found this useful. |
Mar 17 |
reviewed | Close Ideals with norm in arithmetic progression |
Mar 16 |
reviewed | No Action Needed van der Corput lemma for oscillatory integrals |
Mar 16 |
comment |
Number of representations of an integer as an (arbitrary) sum of products
One can get an asymptotic formula for problems like this by using the saddle point method. This is classical, but one reference may be these course notes: math.berkeley.edu/~moorxu/oldsite/notes/155/155main.pdf , see page 44 and following. That deals with the partition problem with generating function $\Gamma(s)\zeta(s)\zeta(s+1)$ (see page 47); you need to make similar calculations with $\Gamma(s)\zeta(s)^2\zeta(s+1)$. There won't be the modular forms miracle as with partitions, but one doesn't need that for an asymptotic. |
Mar 15 |
comment |
When does Merten's product theorem accurately estimate the number of coprimes in an interval?
I don't have access to this from home. If I look at it at work next week (and find time), I'll let you know. |
Mar 15 |
reviewed | Leave Closed Which mathematical ideas have done most to change history? |
Mar 15 |
comment |
A variant of an Eventown problem for modulo a prime number
@AndresCaicedo: I'm not sure I understand your comment. The problem at hand is a special case of the Frankl-Wilson theorem where intersections lying in any set $L$ are considered. So the Frankl-Wilson theorem gives the upper bound I stated (which is not too bad). Of course this upper bound is best possible in general, but not necessarily in this case (and I don't know what the correct result here should be). |
Mar 14 |
comment |
A variant of an Eventown problem for modulo a prime number
There are results in this direction known as the nonuniform Ray Chaudhuri--Wilson theorem (proved by Frankl and Wilson extending work of Ray Chaudhuri and Wilson). This produces an upper bound of $\sum_{s\le n/p} \binom{n}{s}$, which is a step in the direction you want... . |
Mar 14 |
reviewed | Close Can there be a measurable set that integrals have the same given value if their integral on $\mathbb{R}$ are the same? |
Mar 14 |
reviewed | No Action Needed Neusis constructions |
Mar 14 |
comment |
Neusis constructions
I rolled this back to Gerry Myerson's original version, as requested by user130590. |
Mar 14 |
revised |
Neusis constructions
rolled back to a previous revision |