New posts in Analytic Number Theory

Closed form for $\sum\limits_{n=2}^{\infty}\frac1{n^3-1}$

Riemann $\zeta$ and Chebyshev's estimates

Let $g(k)$ be the greatest odd divisor of $k$ show that $ 0< \sum_{k=1}^n \frac {g(k)}{k} - \frac {2n}{3} \lt \frac 23$

Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$

Some convincing reasoning to show that to prove that Ramanujan tau function is multiplicative is very difficult

Riemann zeta for real argument between 0 and 1 using Mellin, with short asymptotic expansion

M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

Convergence of an integral involving the radical of an integer versus the convergence of $\int_2^\infty\frac{dx}{x(\log x)^2}$

What is the intuition for $p$-adic numbers in wiki-sense?

Searching for numbers like $4\times (102564)=410256$