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Results tagged with diophantine-approximation
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user 37555
11
votes
Lower bound for the fractional part of $(4/3)^n$
A non-trivial lower bound can be obtained using linear forms in $p$-adic logarithms. Suppose that $\left\{\left(\frac{4}{3}\right)^n\right\}$ is small. Clearly it is a rational number with denominator …
3
votes
Bounds on near-zero integer linear combinations of numbers linearly independent over $\mathb...
There is a lower bound $f(N)>N^{N-101}$. To see this suppose without loss that $\alpha_1=1$. Then consider all the $N^{N-1}$ values of $\sum_{i=2}^{N} m_i\alpha_i\bmod 1$ with $|m_i|\leq N/2$. There i …