9,685 reputation
13556
bio website research.microsoft.com/~cohn
location Cambridge, MA
age 40
visits member for 4 years, 4 months
seen 8 hours ago

Jun
22
comment polynomial with rational coefficients
@ToddTrimble: I see how to do this if $f(n)$ is an integer for all $n$, but how do you handle the case where this is true for some arbitrary infinite set? (I may be missing something obvious.)
Jun
22
comment polynomial with rational coefficients
Maybe I'm missing a nice way to do it via calculus of finite differences, but that feels like overkill to me. If $f$ has degree $d$, then it's determined by its values at $d+1$ points, and polynomial interpolation preserves rationality.
May
25
awarded  Enlightened
May
24
awarded  Nice Answer
May
24
answered Can the Legendre symbol be calculated in polynomial time?
May
17
comment What is known about $\displaystyle \sum_k{a^{b^k}}$?
If $b$ is an integer and $a$ is the reciprocal of an integer, then you get a beautiful continued fraction expansion (see the articles dx.doi.org/10.1016/0022-314X(79)90040-4 and dx.doi.org/10.1016/0022-314X(82)90047-6 by Jeffrey Shallit).
Apr
23
comment Is anything known about which numbers appear in the continued fraction expansion of $\pi$?
Hopefully someone can expand on this (to make it more suitable as a formal answer), but the quick version is yes: (a) and (b) were true in 1978 and remain true today.
Apr
21
comment Why can't there be a problem both in P and NPC
You're right that the illustration you link to assumes that P ≠ NP. Note that on the P versus NP Wikipedia page, it has the caption "Diagram of complexity classes provided that P ≠ NP."
Apr
19
awarded  Enlightened
Apr
18
revised I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
corrected reference, added link
Apr
18
awarded  Nice Answer
Apr
18
revised I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
made continuity hypothesis explicit
Apr
18
answered I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
Apr
15
comment Limit of distance between two random points in a unit-radius $n$-sphere
I'm not sure there's such a contrast between cubes and spheres. In high dimensions a unit cube is vastly larger than a unit sphere, as measured by diameter or volume, so it's not as fair a comparison as the word "unit" suggests.
Apr
12
comment Geometric explanation of Hutton's formula?
Roger Nelsen gave a proof without words in Math Magazine 86 (2013), 350. See www.jstor.org/stable/10.4169/math.mag.86.5.350.
Mar
21
answered Theta series for the Leech lattice
Mar
18
awarded  Yearling
Mar
17
answered Inequality for Laguerre polynomials
Mar
16
comment Analogues of P vs. NP in the history of mathematics
I didn't downvote it myself, but since no other explanation seems to be forthcoming: the runtime fence problem for TMs fails to satisfy Scott's second criterion ("Mathematicians conjectured that the two classes were unequal, but were unable to prove or disprove that for a long time..."), since Viola gave a proof 20 minutes after you posted the question on cstheory.stackexchange.com. I don't really understand what you mean by the runtime fence problem for languages, but it apparently doesn't satisfy the third criterion ("Eventually, the conjecture was either proved or disproved").
Feb
11
comment What does a Zonal sphere harmonic look like?
Is there an explicit formula for the $L^p$ norms of zonal spherical harmonics? The paper faculty.fiu.edu/~decarlil/Preprints/Proc4.pdf proves estimates for them, which suggests that no such formula is known.