5 problems

For an integer $n$ written as $n=\delta+h(q-1)$ by Euclidean division by $q-1$, define … and let $P_n(x)$ be … Let $\zeta_C^*(-n)$ be the first nonzero coefficient in the expansion…

Let $Z(x,n)$ be written uniquely as … in $A[\![x-1]\!]$, with $h_n\geq 0$ and $\zeta_C^*(n)\in A$. Let $\operatorname{Cl}(\underline{A}(n))$ denote the class module of the Carlitz…

Powers-of-coefficients conjecture. For any $i,j,m,n$, there exists $\gamma\in\mathbb{N}$ such that

Let $K$ be the rational function field used in the Carlitzian setting, and let $\widehat{\pi}$ be the associated Carlitz period analogue. Transcendence conjecture. The element…

Let $n>0$ and $s\geq 0$ be integers. Write the base-$q$ expansion of $n$ as $n=n_0+n_1q+\cdots+n_rq^r$ and set $\ell_q(n):=\sum_i n_i$. For the finite zeta value of level $s$ and e…