30,225 reputation
695157
bio website math.harvard.edu/~elkies
location Harvard University, Cambridge, MA 02138
age 47
visits member for 3 years, 2 months
seen 4 hours ago
[Not sure yet what to use this space for...]

1d
awarded  Good Answer
Jul
22
revised Is this divisor ample on the product of two curves
added 187 characters in body
Jul
22
comment Is this divisor ample on the product of two curves
Thanks. I see that this was in fact a "Community" action. This question's score was zero, not positive, but the page you linked to says "non-negatively scored" so a score of zero still fits that criterion.
Jul
22
comment True or false: if a set of 2D points has valid symmetry axes, then at least one of them is equal to a principal component vector
In practice this will usually work, but if the covariance matrix is scalar (or numerically indistinguishable from scalar) then every line through the origin is still a candidate symmetry axis.
Jul
22
answered Is this divisor ample on the product of two curves
Jul
21
awarded  Custodian
Jul
21
reviewed Leave Open How $f$ is approximated, in the $L^{p}-$ norm, by a function $f+h$ whose Fourier transform is constant in some nbhd of the point?
Jul
21
reviewed Leave Open Complex Phase Problem Relating to Binary Quadratic Forms
Jul
21
reviewed Reviewed BMO spaces on the torus
Jul
18
comment Magic squares with specific properties
For $n=3$ there's a 5-dimensional (affine) space of solutions, and it seems that generically there's no other subset that sums to $1$, so as long as you avoid a finite number of hyperplanes you're fine.
Jul
15
comment minimal conductors among elliptic curves with a fixed CM type
A bit more precisely, an elliptic curve has CM not by $K$ but by some order in $K$, i.e. a finite-index subring of $O_K$. Usually that order must be $O_K$ itself, but there is one more choice for $d=-4$ and $d=-7$, and two more for $d=-3$. In all but one of these four extra cases, specifying the CM ring does not affect the answer, because there's always a minimal-conductor curve with endomorphisms by $O_K$ that's isogenous to $E$ (and isogenies preserve the conductor). But for $d=-3$ there's an index-2 subring ${\bf Z}[\sqrt{-3}]$ of $O_K$ whose minimal conductor is not $27$ but $36$.
Jul
13
revised Incomplete Kloosterman sum
added 601 characters in body
Jul
12
comment Incomplete Kloosterman sum
…and there's a stray ")" in each instance of the denominator $e(b)-1$.
Jul
12
awarded  Nice Answer
Jul
12
answered Incomplete Kloosterman sum
Jul
10
answered A calculation involving Lerch Transcendents
Jul
8
answered Union of conjugates of a closed subgroup of a compact group
Jul
7
comment Points with minimal height
That looks as hard as deciding the existence of a rational point on an arbitrary variety $V/K$. Having found one $\phi(\beta)$ of low height, you can effectively find all points of lower height, but the preimage of each one is some variety $V/K$, and finding a rational point on $V$ is a system of Diophantine equations that can be as intractable as you wish. (It must be possible to rig things so that there's only one plausible candidate of height lower than $\phi(\beta)$ and this candidate yields your favorite $V$.)
Jul
7
comment Finding the set of all $0-1$ vectors in an affine subspace
For a finite projective plane (whether classical or not) there can't be any solution, because you're asking for a set $S$ of points that meets every line in just one point, but then $|S|>1$ and the line through any two points of $S$ yields a contradiction.
Jul
7
answered intersection of the unit cube and a hyperplane containing the main diagonal