Research proof index

An approximate-homomorphism theorem for finite elementary abelian $2$-groups. Let $f:G\to G'$ and $K>0$. If at least a proportion $K^{-1}$ of pairs $(x,y)\in G^2$ satisfy $f(x+y)=f(x)+f(y)$, then there are an additive homomorphism $\varphi:G\to G'$ and a constant $c\in G'$ such that $f(x)=\varphi(x)+c$ for at least $|G|/(2^{144}K^{122})$ values of $x$.

The L-series of d k equals ζ(s)^k for Re(s) > 1.

If g is a multiplicative arithmetic function, then for any $n \neq 0$, $\sum_{d | n} \mu(d) \cdot g(d) = \prod_{p | n} (1 - g(p))$.

The k-th coefficient (k < deg φ) of a gadget-decomposition block is exactly the corresponding digit of the corresponding input coefficient.

The base-b gadget decomposition is a lawful gadget decomposition.

Each gadget-decomposition block is ℓ₂²-short: its centered squared-ℓ₂ norm is at most (deg φ)·(b-1)² (each of the deg φ coefficients contributes at most (b-1)²).