bio  website  math.tsukuba.ac.jp/~carnahan 

location  筑波市, Japan  
age  
visits  member for  4 years, 6 months 
seen  43 mins ago  
stats  profile views  15,306 
I think this is a neat project.
1d

comment 
some question about Geometric invariant theory
Please see meta.mathoverflow.net/questions/70/howtoaskpage before revising your question. 
1d

comment 
Journals dedicated towards work exploring the development of toy systems of axioms?
You may want to look at some examples of weak systems of arithmetic listed at en.wikipedia.org/wiki/Ordinal_analysis 
1d

comment 
A nonliner second order differentice equation with two parameters
Please see meta.mathoverflow.net/questions/70/howtoaskpage 
Apr 18 
reviewed  Reject suggested edit on Distance between poisson points in two disjoint unit discs 
Apr 18 
comment 
lfunctions of calabiyau varieties
Have you tried searching the web for terms like "mirror symmetry" and "lfunction"? See Theorem 9.5 in math.rochester.edu/people/faculty/chaessig/mirror.pdf 
Apr 17 
revised 
The problem of Riemann zeta function
rolled back to a previous revision 
Apr 16 
awarded  Enlightened 
Apr 16 
awarded  Nice Answer 
Apr 16 
comment 
Information geometry divergence
Please explain what you want to do in your own words. 
Apr 16 
comment 
How to prove that every polynomial in an infinite family is irreducible over Q?
I'm not sure I understand your question, but it looks like you are asking about the polynomials given by choosing integer values for $y$. For any choice of $y$, you can choose a valuation using the largest prime dividing $y$, and construct the corresponding Newton polygon. My wild guess is that it should be possible to reason about this polygon without much explicit knowledge about $y$, e.g., if $y$ is not a power of 2, then perhaps the polynomial can only split as a linear factor times a quartic. 
Apr 16 
comment 
Weyl algebras $A_n(k)$ as tensor product of the first Weyl algebra
How are you presenting these Weyl algebras? 
Apr 16 
comment 
How to prove that every polynomial in an infinite family is irreducible over Q?
Can you use the Newton polygon for the largest prime dividing $y$ to eliminate the possibility of a cubic times a quadratic? 
Apr 15 
comment 
On the schur Multiplier of a group
You should read ATLAS page XX again, and review the meaning of $2.G$. 
Apr 15 
comment 
What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
@Anush Yes. The OP's exponent is precisely what is needed to cancel the $n \log 2$ from $\log \binom{n}{2k}$ for optimal $k$. This is why I needed to consider the subleading term with the $\pi c$ computation. If the exponent is smaller, the sums diverge even more wildly, and if the exponent is larger, the sums converge to 1. 
Apr 15 
comment 
What are the modular transformation properties of qPochhammer symbols?
Instead of $z^{12}$, do you mean $e^{(z+1/z)i\pi/12} \sqrt{iz}$? That seems to be what comes out of en.wikipedia.org/wiki/Dedekind_eta_function 
Apr 15 
comment 
What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
@GregMartin You're right, thanks. I've made quite a mess of this question. 
Apr 15 
revised 
What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
More sign errors 
Apr 14 
revised 
What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
Sign error in log binomial 
Apr 14 
revised 
What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
More explicit estimates. 
Apr 13 
comment 
What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
@Anush Yes. In the fourth expansion of my list, the optimal coefficient of $n$ is about $0.14676$, and the coefficient of $n$ from the fifth sum is $\log 2$. Thus, if you divide the exponent by more than about 4.722967, the limit diverges. [Edit: this is not accurate  see later comments.] 