MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

# i707107

 1,034 Reputation 932 views

## Registered User

 Name i707107 Member for 1 year Seen 1 hour ago Website Location United States Age 30
 Jun5 comment Minimal representation of a polynomial as a linear combination of squaresThanks, I got it now. It can also be done by induction on degree. Jun5 comment Minimal representation of a polynomial as a linear combination of squaresWhy does $h$ have degree at most $n-1$? I know that it should be $\leq 2n-1$, but how do you get $n-1$? Jun2 comment Minimal representation of a polynomial as a linear combination of squaresWhen it is reducible with $f=uv$, and degree of $u$, $v$ are $n$, then $p=((u+v)/2)^2-((u-v)/2)^2$. But, not sure how to go for other cases. Jun2 comment Sums of inverse determinants over matricesI think the true bound is $S(r)=O(r^2\log r + r^3)$ now. Jun2 comment Sums of inverse determinants over matricesI realized that that estimate was overestimate. This is a counting argument for lattice points, like one uses for Gauss Circle Problem. The number of lattice points inside a convex region is approximated by the area of the region + error term depending on perimeter. Jun1 comment Sums of inverse determinants over matricesArgument seems to work in general, $S(r)=O(r^{n^2-1}\log r)$. Jun1 answered Sums of inverse determinants over matrices Jun1 comment How does Yitang Zhang use Cauchy’s inequality and Theorem 2 to obtain the error term coming from the $S_2$ sumYes, your outline precisely is C-S. But mine is truncation of sums, so I would have $\sum x_iy_i\leq K\sum x_i+K^{-1}\sum x_iy_i^2$, since the first sum on the RHS is upper bound for the sum of terms with $y_i\leq K$, and the second sum on the RHS is for $y_i>K$. May31 comment How does Yitang Zhang use Cauchy’s inequality and Theorem 2 to obtain the error term coming from the $S_2$ sum@GH: Good point! I tried reproducing proof of C-S regarding your comment, but misses a factor of 2. So, this method overestimates than C-S by a factor of 2. May31 answered How does Yitang Zhang use Cauchy’s inequality and Theorem 2 to obtain the error term coming from the $S_2$ sum May29 comment A technical question related to Zhang’s result of bounded prime gaps@ericc: Edited. Implemented your correction, and simplified a little. I did not need to have $d=d_0 k$, since what I needed is $d$ having many prime factors. May29 revised A technical question related to Zhang’s result of bounded prime gapssimplified argument, implemented comment by ericc May29 comment A technical question related to Zhang’s result of bounded prime gaps@ericc: Yeah, I missed that. The extra $\tau_{k_0}(d)$ will give extra powers of $\mathcal{L}$ on the numerator. But, my argument still works as you noticed. May29 accepted A technical question related to Zhang’s result of bounded prime gaps May28 answered A technical question related to Zhang’s result of bounded prime gaps May25 accepted Any closed form for series like $F(x)=\Sigma_{i=p}^{\infty}x^p$,p is prime$? May24 comment Any closed form for series like$F(x)=\Sigma_{i=p}^{\infty}x^p$,p is prime$?Hold for series convergent with radius 1. Any series obtained from your setting, will have radius of convergence 1, or infinity. The case when radius of convergence infinity, is only when $r$ has finite decimal expansion. May24 comment Full $n$-torsion of elliptic curves and the cyclotomic field of order $n$Yes. Weil pairing applies to $n$-torsion too. May24 comment Any closed form for series like $F(x)=\Sigma_{i=p}^{\infty}x^p$,p is prime$?As I mentioned in my answer,$r$can be either rational or irrational. When$r$is rational, the function$f$is rational, and when$r$is irrational, the function$f$is transcendental. May24 comment Any closed form for series like$F(x)=\Sigma_{i=p}^{\infty}x^p$,p is prime$?This might be better expression: $$\sum_{p\textrm{ prime}} x^p$$ May24 revised Any closed form for series like $F(x)=\Sigma_{i=p}^{\infty}x^p$,p is prime$?added 74 characters in body May24 answered Any closed form for series like$F(x)=\Sigma_{i=p}^{\infty}x^p$,p is prime$? May16 comment Ramification in Division field of Abelian Varieties Maybe I should have put, $m$ avoids all primes of bad reduction. May16 comment Ramification in Division field of Abelian Varieties Thank you. This is also very clear. So $\mathbb{Q}(E[2])=\mathbb{Q}(\sqrt{d})$, and primes ramify in $\mathbb{Q}$ are precisely the prime divisors of $d$. May16 comment Ramification in Division field of Abelian Varieties Thank you for clear counterexample. I'd like to know what happens when $m$ is a power of $p$. May16 asked Ramification in Division field of Abelian Varieties May15 comment Sums of uniformly random vectors from the $n$-dimensional unit ballTo clarify: $||v_i||\leq 1$ right? not $||v_i||=1$? May9 comment Least prime in an arithmetic progression and the Selberg sieveWhat is $\tau$ in the last formula? Is it the "number of divisors" function? May8 comment The classifying space of a gauge groupIt is also strange that LaTeX is completely working on my iPhone, but not on PC. May8 comment Functional equationsOr, are those separate problems? May8 comment Functional equationsPutting $x=y=z$, you get $2X^2=1$, and $X^3=1$ where $X=f(x,x)$, which is nonsense. May7 comment average involving phi functionI think so too. May7 comment average involving phi functionIt is also possible to obtain an asymptotic formula with main term $C\frac{1}{\log N}$ for some positive constant $C$. Apr20 comment Efficient (divergent) summation for sum of zetas at negative arguments?See this: wolframalpha.com/input/… Apr20 comment Efficient (divergent) summation for sum of zetas at negative arguments?That must be an error, this function does have limit as $s\rightarrow 0$, and it is $1+\zeta'(0)$. Apr19 answered Efficient (divergent) summation for sum of zetas at negative arguments? Apr19 comment Efficient (divergent) summation for sum of zetas at negative arguments?I will write proof of $m=-1$ case as an answer. Apr19 comment Efficient (divergent) summation for sum of zetas at negative arguments?Using that $\zeta'(0)=-\frac{1}{2}\log 2\pi$, I could prove that the approximation you have is correct. Apr19 comment Efficient (divergent) summation for sum of zetas at negative arguments?So, for $m=-1$, did you prove it? or is it just a numerical approximation? Apr19 comment When integer polynomials take integer values, does their GCD also take integer values?Yes, but I am pointing out that the GCD should be considered as UFD element. In particular in $\mathbb{Z}[x]$, the GCD of $P$, and $Q$ is, some integer multiple of OP's definition. For example, GCD of $2x^2$ and $8x^2+4x$ is $2x$. Apr8 revised Ordinary Generating Function for Mobiusadded 202 characters in body Apr8 revised Ordinary Generating Function for Mobiusdeleted 204 characters in body Apr8 revised Ordinary Generating Function for Mobiusadded 198 characters in body; added 12 characters in body Apr8 revised Ordinary Generating Function for Mobiusadded 386 characters in body Apr7 revised Ordinary Generating Function for Mobiusadded ; added 30 characters in body; added 11 characters in body; added 10 characters in body; deleted 4 characters in body Apr6 awarded ● Critic Apr3 asked Ordinary Generating Function for Mobius Mar22 answered $\prod_{n=1}^{\infty} n{}^{\mu(n)}=\frac{1}{4 \pi ^2}$ Mar11 answered Expression for the sum of square roots of zeros of a polynomial Mar8 revised Invertibility of a certain matrix indexed by the Hamming cubeAdded a comment about inverse.