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bio website math.harvard.edu/~elkies
location Harvard University, Cambridge, MA 02138
age 49
visits member for 4 years, 4 months
seen 6 hours ago
[Not sure yet what to use this space for...]

16h
comment 2-dimensional sublattices with all vectors having very big square (in absolute value)
But then it feels like the $N \cdot H$ construction or something much like it does work even when $\Lambda$ is not unimodular.
1d
comment 2-dimensional sublattices with all vectors having very big square (in absolute value)
In any case this approach must fail in rank $n=3$ because then there are only finitely many $N$ for which a lattice of the form $N\cdot H$ can embed primitively into $\Lambda$.
1d
comment Zero divisors with support of size 3 in group algebras of finite groups
Yes: let $G = \langle g \mid g^7 = 1 \rangle$ and $\alpha = g + g^2 + g^4$; then $\alpha (\alpha+1) = 0$.
2d
answered What is $\sum (x+\mathbb{Z})^{-2}$?
2d
awarded  Enlightened
2d
awarded  Nice Answer
2d
awarded  Necromancer
2d
accepted The coupon collector's earworm
2d
comment The coupon collector's earworm
@kantelope try the new faster code.
2d
comment The coupon collector's earworm
@Steven Stadnicki - I hadn't checked The Art Of Computer Programming; that's a good idea, but I cannot locate the problem in either the main text or the exercises. Were you able to find it there?
2d
revised The coupon collector's earworm
edited mostly to report on the answer by **Kevin Costello** (and to improve the **gp** code at the end)
2d
revised Does there exist a nonconstant, periodic, real analytic function with period 1 and rational Maclaurin coefficients?
minor edits
Aug
31
awarded  Necromancer
Aug
31
awarded  Revival
Aug
31
answered Does there exist a nonconstant, periodic, real analytic function with period 1 and rational Maclaurin coefficients?
Aug
30
comment Congruences involving binary forms and primes of the form $x^2+y^2$
It might still help to see the original congruence, which could be more tractable than the form involving $\sum_{k=0}^s \left({s+k\atop k}\right) 2^k$.
Aug
29
comment The coupon collector's earworm
Thanks for this as well. I expect that I'll "accept" your answer soon (I already "up-voted" it), and will edit the question to reflect your answer.
Aug
29
comment The coupon collector's earworm
Thanks for this analysis; the appearance of $e$ as the asymptotic coefficient of $\log N$ is unexpected, and the results you quote almost give the asymptotic behavior of $M_N$ en route to describing the distribution near $e \log N$. I write "almost" because the distribution could be asymptotically concentrated at $e \log N$ but still have a heavy enough tail to shift the mean $M_N$ above $(e+o(1)) \log N$. Usually such "concentration" results come with error estimates that force the mean and mode to be quite close; is this the case here too?
Aug
28
awarded  Good Question
Aug
27
comment What is the exact statement of “there are 27 lines on a cubic”?
Even 27 rational lines (still with the same construction).