9 problems

Minimal-polynomial degree conjecture. The degree of a minimal polynomial for the modulus $3^\gamma$ is $2d$.

For each $n$, let $\Delta_n$ denote the relevant $n$-state model space, and let $a_n$ be the number of fundamental models in $\Delta_n$ of degree $2n-1$. For $n\geq 3$, Proposition…

Let $(T,Q)$ be a parameter pair for a recursive sequence, and let the sets of prime divisors of its even-indexed and odd-indexed terms be denoted by $P_{\mathrm{even}}$ and…

M. Stein's conjecture. One has $\dim_{\mathbb{Q}}V_m=m$ for every positive integer $m$. Moreover, for every $\left(t_1,\ldots,t_{4m}\right)\in V_m$,

Let $f\in\mathbb Q(d_1,d_2)$ be a rational function defined on $\mathbb Z^+\times\mathbb Z^+$ and suppose … and … for some $k\in\mathbb R^+$. If $n_d$ is a sequence recursively def…

Let $p$ be prime and let $p^\gamma$, with $\gamma\ge1$, be a modulus. A minimal polynomial is a polynomial of least degree giving the relevant recursive-sequence relation modulo…

For positive integers $b_1,\dots,b_s$, let $H_{b_1,\dots,b_s}(z)$ denote the series used in the paper, and let $H_{a_1,\dots,a_r}(z)$ be the corresponding series with indices $a_i$…

Let $S_{\mathfrak H(q)}(z)$ denote the generating function for the subgroup numbers of the Hecke group $\mathfrak H(q)$. For a positive integer $h$, define … Let $\alpha$ be a posi…

Let $\mathcal{A}=(a_1,a_2,\dotsc)$ be a sequence of numbers in $(1,\infty)$, and let Proposition deterministically construct a sequence $\mathcal{X}=(x_0=0,x_1=1,x_2,\dotsc)$ from…