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visits | member for | 1 year, 11 months |
seen | 9 mins ago | |
stats | profile views | 7,994 |
Mar 26 |
reviewed | Leave Open How good is “almost all” when it comes to the Riemann Hypothesis? |
Mar 26 |
awarded | Enlightened |
Mar 26 |
awarded | Nice Answer |
Mar 26 |
revised |
Measure of a set of irrational numbers
added 411 characters in body |
Mar 26 |
revised |
Measure of a set of irrational numbers
added 411 characters in body |
Mar 26 |
comment |
Measure of a set of irrational numbers
From properties of continued fractions one knows that $|x-p_n/q_n|$ is roughly $1/(q_nq_{n+1})$ and also $q_{n+1}$ is roughly $a_{n+1}q_n$. So the LHS of the last inequality is about $C/(q_n^2 a_{n+1})$ and now you get that $a_{n+1} \ge c n$. Does that make sense? |
Mar 26 |
answered | Measure of a set of irrational numbers |
Mar 25 |
comment |
Number of representations of an integer as an (arbitrary) sum of products
I think my answer below provides a complete solution to your problem. Were you looking for something more? Or perhaps there was something unclear with what I wrote? |
Mar 25 |
reviewed | Close Curves of high genus with many rational points |
Mar 24 |
reviewed | Leave Open Consecutive non-quadratic residues |
Mar 24 |
awarded | Enlightened |
Mar 23 |
revised |
maximum size of intersecting set families
added 761 characters in body |
Mar 23 |
comment |
Ramanujan's tau function
Also Ramanujan was interested in representations of numbers by quadratic forms, and in particular the number of representations of an integer as the sum of an even number of squares. Exact formulas were known in a number of cases already, and he might have been trying to extend these. As I recall, his famous paper begins by writing down identities for the products of Eisenstein series, and records the first case where one doesn't have an exact identity, and this comes from the tau function. |
Mar 23 |
answered | maximum size of intersecting set families |
Mar 23 |
comment |
maximum size of intersecting set families
Every $k$ element set has $\binom{k}{2}$ subsets of size $2$, and all the subsets of size $2$ from the $m$-sets we have should be distinct. Therefore $m\binom{k}{2} \le \binom{n}{2}$, or $m\le n(n-1)/(k(k-1))$. Are you looking for such upper bounds for $m$, or for constructions giving lower bounds for $m$? |
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 |