Pellarin's Identity, Carlitz Period, and Anderson Generating Functions over Arbitrary Curves

Let \(A\) be the coefficient ring of a smooth projective curve over \(\mathbb{F}_q\) with a closed point at infinity of arbitrary degree \(\mathrm{N}=°(\infty)\ge 1\), and let \(φ\) be a rank-one Drinfeld \(A\)-module. In this paper, we prove three main results concerning the module of special funct