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Results tagged with transcendental-number-theory
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user 120369
0
votes
1
answer
176
views
Any ideas for the following limit of partial sums of binomial coefficients?
Let $a$ be an odd integer $≥3$. It appears that: $$\lim_{n\rightarrow\infty}\frac{1}{2^{n}}\sum_{m=0}^{\left\lfloor n\frac{\ln2}{\ln a}\right\rfloor }\binom{n}{m}=\begin{cases}
1 & \textrm{if }a=3\\
0 …
- 12.8k
12
votes
1
answer
1k
views
Is the p-adic Lindemann-Weierstrass Conjecture still open?
The p-adic Lindemann-Weierstrass Conjecture: Let $\alpha_{1},\ldots,\alpha_{N}\in\overline{\mathbb{Q}_{p}}$
be distinct $p$-adic algebraic numbers satisfying $\left|\alpha_{n}\right|_{p}<p^{-\frac{1 …
- 1,284