27,364 reputation
150117
bio website math.tsukuba.ac.jp/~carnahan
location 筑波市, Japan
age
visits member for 4 years, 6 months
seen 43 mins ago
I think this is a neat project.

1d
comment some question about Geometric invariant theory
Please see meta.mathoverflow.net/questions/70/how-to-ask-page 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 non-liner second order differentice equation with two parameters
Please see meta.mathoverflow.net/questions/70/how-to-ask-page
Apr
18
reviewed Reject suggested edit on Distance between poisson points in two disjoint unit discs
Apr
18
comment l-functions of calabi-yau varieties
Have you tried searching the web for terms like "mirror symmetry" and "l-function"? 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 sub-leading 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 q-Pochhammer 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.]