5 problems

Congruence-restricted $\tau$-hypothesis. There is an absolute constant $c_p>0$ such that, for every $f\in\mathbb{Z}[x_1]\setminus\{0\}$, the number of such roots is at most

Shub–Smale $\tau$-conjecture. There is an absolute constant $\kappa\geq 1$ such that, for every $f\in\mathbb{Z}[x_1]\setminus\{0\}$, the number of distinct roots of $f$ in…

Additive-complexity regularity conjecture. The sequence $(\rho^+_{\mathbf{w}}(n))_{n\geq 1}$ is $k$-regular.

Let a splice of finitely many infinite words be a word formed by successively taking finite blocks from each constituent word, with the concatenated blocks from each constituent fo…

Let $\mathcal{A}_{k,a}$ be the family of ordered finite lists $\mathcal{P}=(P_1,\ldots,P_s)$ of polynomials in $\mathbb{R}[X_1,\ldots,X_k]$, with total additive complexity at most…