TravorLZH

### Answers (93)

 7 Contour integration w/ exponential and cosine functions 4 Simplest proof that $\sum 1/p$ grows like $\log \log x$ 4 Properties of Chebyshev’s $\psi$ Function 4 Evaluating $\sum _{k=1}^{\infty }\frac{H_k}{4^k\left(2k+1\right)}\binom{2k}{k}$. 3 Limit of $\frac{\sum_{i=1}^{n}{(n \mod i)}}{n^2}$

### Reputation (1,853)

 +30 Limit of $\frac{\sum_{i=1}^{n}{(n \mod i)}}{n^2}$ +25 Last step in Apostol's Section 11.6 Lemma 2 (Dirichlet Series) +10 Elementary method to prove that $|\overline B_{2n}(x)|\le|B_{2n}|$? +10 Partial summation of $d(n)/(n-1)$

### Questions (22)

 4 On the asymptotic bound for $\arg\zeta(s)$ on the critical line 3 On the Mellin transform of logarithmic integral 3 On an integral related to the prime number theorem 3 On the asymptotic behavior of Elliptic integral near $k=1$ 3 Show that this sequence of functions converges uniformly to $e^{-x}$

### Tags (95)

 38 analytic-number-theory × 51 11 sequences-and-series × 8 36 number-theory × 32 11 elementary-number-theory × 7 24 integration × 14 10 complex-numbers × 2 18 complex-analysis × 19 9 asymptotics × 12 11 calculus × 18 9 real-analysis × 12

### Bookmarks (3)

 6 Integrate $\frac{\log(x^2+4)}{(x^2+1)^2}$. 5 Proving $\dfrac{4}{\pi}\sum_{k = 1}^{\infty}\dfrac{(-1)^{k - 1}k}{B_{2k}(2k - 1)}\left(\dfrac{\log n}{2\pi}\right)^{2k - 1} = \dfrac{n}{\text{In}n}$ 2 Deriving Selberg's asymptotic formula from Selberg's identity

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