4 problems

Let $E$ be the Anderson $t$-module under consideration over $L/K$, let $P$ be a prime of $A$, and let $\Omega_E$ be the period lattices associated with $E$. Write $r_{\Omega_E}$ fo…

Let $E$ be the Anderson $t$-module under consideration, let $P$ vary over primes of $A$, and define the order of vanishing of the $P$-adic $L$-series at $z=1$ by … to be the greate…

Let $E$ be an Anderson $t$-module, let $P$ be a prime of $A$, and define … and … Also write $\mathscr{U}(E;\mathscr{O}_L)=\exp_E(U(E;\mathscr{O}_L))$. Leopoldt conjecture. The…

Injectivity conjecture. The $P$-adic $L$-series is non-zero if and only if the exponential map $\exp_E:L_\infty^d\rightarrow L_\infty^d$ is injective.