MathOverflow

While experimenting with hypergeometric-style sums, I came across the following identity.
For integers $a\ge 1$, $b\ge 0$, $c\ge a+b$, and all $n\ge 0$ (with the convention $1/(-k)!=0$, so the LHS vanishes for $0\le n<b$),$$\begin{aligned}\left(\frac{(2n+a)!}{(n-b)!\,(n+c)!}\right)^{\!2}\;=\;\sum_{k=\lfloor a/2\rfloor+1}^{c}&\!\left...

There are multiple results on the sieve method, and I wanted to ask about the following variant(to know if it is trivial by one of the current versions of the sieve method, or seems a challenging problem)
Let $\varepsilon>0$ be fixed.Then there exists $0<\delta<\varepsilon$, such that for all sufficiently large $k$ the following is true....

I’ve been thinking about the following type of equation.Let( A = {a_1,\dots,a_c} ), ( K = {k_1,\dots,k_m} \subset \mathbb{N} )be finite nonempty sets such that:• elements in each set are distinct,• ( A \cap K = \varnothing ),• for any distinct (x,y ...

Has anyone reviewed this recent paper claiming to prove the Riemann Hypothesis?Title: The Adelic Quantum Graph: A Self-Adjoint Realization of the Riemann Zeros
https://zenodo.org/records/19634443