15,569 reputation
14184
bio website zakuski.math.utsa.edu/~jagy
location Berkeley, California
age 58
visits member for 5 years, 7 months
seen Aug 30 at 2:02
My main activity is in number theory of integral positive ternary quadratic forms. This began through years of working with Irving Kaplansky. Much of his unpublished writing on quadratic forms can be found as pdfs at http://zakuski.math.utsa.edu/~kap/forms.html and about Lie and Jordan superalgebras at http://zakuski.math.utsa.edu/~kap/superalgebra.html One of my own email addresses can be found easily using the search feature at http://www.ams.org/cml and just putting in my last name

Aug
25
comment 2-dimensional sublattices with all vectors having very big square (in absolute value)
Oh, that probably does demand some kind of diophantine approximation argument, then; I don't quite recall what you commented earlier on the proof you found not really to your liking.
Aug
25
comment 2-dimensional sublattices with all vectors having very big square (in absolute value)
seems to me there is a sublattice of dimension $\lceil \frac{n}{2} \rceil$ on which your nondegenerate form is definite. Does that suffice?
Aug
24
comment Generating a series representation for the inverse of the operator $f(f)$
not sure what you mean, but see mathoverflow.net/questions/45608/… and math.stackexchange.com/questions/208996/half-iterate-of-x2c/… and math.stackexchange.com/questions/911818/…
Aug
18
comment constructing koenigs function
@AlexandreEremenko, I see, I think you are referring to the language "infinite subset" used in the question above by james.nixon. I don't know what that means either.
Aug
18
comment constructing koenigs function
@AlexandreEremenko, see the same question and my brief answer at math.stackexchange.com/questions/1397468/… The chapter in Milnor, in the third edition, is chapter 10, Parabolic Fixed Points: The Leau-Fatou Flower. However, the condition here that $|f'(x_0)| > 1$ simplifies matters, we just take a local inverse function, and we do not need the full Ecalle machinery. I'm quite proud of figuring out how to do that, see: mathoverflow.net/questions/45608/…
Jul
30
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p$ and $p$ is an odd prime?
GH thanks anyway
Jul
30
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p$ and $p$ is an odd prime?
GH, do you have any opinion on Noam's variant, $\sigma(x^2) = y^2?$ Noam suggests infinitely many solutions. Gerry wrote me to ask for the Kaplansky preprint mentioned at the OEIS page, Kap (and Dickson, pages 54-58 in volume I of his History) credit the problem to Ozanam. Kap found a way to make a group out of squarefree soluitons $x,$ which increases the number of solutions that one may find but does not appear to make it infinite
Jul
30
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p$ and $p$ is an odd prime?
@Gerry, also sent the one page from Kap's preprint to Noam
Jul
30
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p$ and $p$ is an odd prime?
@Noam, sent you the relevant page from the preprint of Kaplansky that Gerry mentions.
Jul
17
comment Equidistribution of representations by a binary cubic form
GH, thank you. Nice result and conjecture/wonderment, no idea on my part whatsoever.
Jul
17
comment Equidistribution of representations by a binary cubic form
Oh, well. The reason this caught my eye is the well known equidistribution for positive ternary quadratic forms, Duke and Schulze-Pillot. Just a cosmetic resemblance, I suppose.
Jul
17
comment Equidistribution of representations by a binary cubic form
nope, they want a prescription jlms.oxfordjournals.org/content/s2-28/1/1.full.pdf+html
Jul
17
comment Equidistribution of representations by a binary cubic form
getting there, jlms.oxfordjournals.org/content/s2-28/1.toc
Jul
17
comment Equidistribution of representations by a binary cubic form
i see; finite because of Thue, chapter 22 in Mordell's book. Could you please summarize the Silverman theorem you reference?
Jul
17
comment Determinant of a Certain Positive-Definite Block Matrix
crosspost math.stackexchange.com/questions/1330576/…
Jul
17
comment Asymptotic behavior of the minimum eigenvalue of a certain Gram matrix with linear independence
crosspost math.stackexchange.com/questions/1350777/…
Jul
14
comment how to determine a biquadratic form is positive-definite
Thanks. I can give a pretty good string of examples by a different guy, at what I suspect is a similar level. Here is the sixth question on a variant of Hadamard matrices math.stackexchange.com/questions/1359986/… where the initial post allowed entries $1,0,-1$ in the matrices. If you look at all his questions, it just appears that he is crowdsourcing something like a Master's project instead of doing anything himself, including simple computer runs for $n$ by $n$ examples with $n$ smaller
Jul
14
comment how to determine a biquadratic form is positive-definite
Noah, see math.stackexchange.com/questions/1352115/… I just logged on here, but i would guess the close votes are about a question in an unfamiliar area, with a fishing expedition for iff results, by someone who shows no evidence of research background or effort.
Jul
12
comment Approximating a real by a ratio of primes
@JosephO'Rourke, the term mediant is used in simple continued fractions, it is exactly how two consecutive "convergents" are combined to make the next one when the "digit" $a_i$ is $1.$ When the digit is larger than $1,$ the actual combination can be repeated by repeated mediant with the second convergent. This is in Khinchin's little book; he gives no name to my digits $a_i,$ some authors say "partial quotients"
Jul
3
comment Non-Forking and Related Concepts
I see, not actually en.wikipedia.org/wiki/Forklift_truck