# Tagged Questions

**15**

votes

**1**answer

849 views

### Quantitative lower bounds related to Zhang's theorem on bounded gaps

Let $\mathcal{H}=\left\{ h_{i}\right\} _{i=1}^{k}$ be an admissible set, and define $$\pi_{\mathcal{H}}(x)=\left|\left\{ n\leq x\ :\ \exists\ i,j\leq k,\ i\neq j\ \text{such that both }n+h_{i},\ ...

**3**

votes

**2**answers

449 views

### Lower bound for Euler's totient for almost all integers

Let $\varphi(n)$ be the Euler's totient function. It is well know that $\liminf_{n \to \infty} \frac{\varphi(n)}{n / \log \log n} = e^{-\gamma}$, so that for $\varepsilon > 0$ it results ...

**8**

votes

**0**answers

539 views

### Lower bounds for linear forms of logarithms (a la Baker)?

Let $\lambda_1$, $\lambda_2$, and $a$ be three fixed complex algebraic
numbers.
For a given integer $n$, write
$\Theta(n) = \arg(a \lambda_1^n + \lambda_2^n)$.
Assuming $\Theta(n)$ is not zero, I am ...